Faculty

Kalyana Babu Nakshatrala, Ph.D.
Dr. Kalyana Babu Nakshatrala, Ph.D.
Assistant Professor
Office Location: N124 Engineering Bldg 1, Houston, TX 77204-4003
Phone: 713-743-4418 | Fax: 713-743-4260
Email: knakshatrala [at] uh [dot] edu

Education: 

Doctor of Philosophy, Civil & Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois, May 2007. (Major: Structural Engineering, and Certificate in Computational Science and Engineering)
Master of Science, Applied Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois, May 2007.
Master of Science, Civil & Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois, May 2002.
Bachelor of Technology, Civil Engineering, Indian Institute of Technology-Madras, Chennai, India, May 2000.

Professional Experience: 

September 2011 - present: Assistant Professor, Department of Civil and Environmental Engineering, University of Houston, Houston, Texas.
April 2012 - present: Assistant Professor, Department of Mechanical Engineering, University of Houston, Houston, Texas.
January 2009 - August 2011: Assistant Professor, Department of Mechanical Engineering, Texas A&M University, College Station, Texas.
June 2007 - December 2008: Postdoctoral Research Associate, University of Illinois at Urbana-Champaign, Urbana, Illinois.
August 2000 - May 2007: Graduate Research Assistant at Center for Simulation of Advanced Rockets (CSAR), University of Illinois at Urbana-Champaign, Urbana, Illinois.

Students Supervised: 

Doctor of Philosophy

 

Year Student Thesis title & Institution
AUG 2015 Maruti MUDUNURU

"On enforcing maximum principle and element-wise species balance for advective-diffusive-reactive systems," University of Houston

Career after degree: Postdoctoral Research Associate, Los Alamos National Laboratory (LANL)

AUG 2016 Mohammed SHABOUEI

"Viscous fingering and mixing in porous media: Scaling laws, stability analysis, and numerical formulations," University of Houston

Career after degree: Postdoctoral Research Associate, University of Notre Dame

DEC 2016 Saeed KARIMI

"Computational methods for multi-scale temporal problems: Algorithms, theoretical analysis, and applications," University of Houston

MAY 2017 Can XU

"Modeling material degradation due to moisture and temperature," University of Houston.

MAY 2017 Justin CHANG

"Stucture-preserving high performance computational methods for transport equations with an emphasis on subsurface applications," University of Houston.

Career after degree: Postdoctoral Research Associate, Department of Computational & Applied Mathematics, Rice University

 

Master of Science (M.S.) with thesis

 

Year Student Thesis title & Institution
MAY 2011 Abhineeth AKKASALE

"Stability of coupling algorithms," Texas A&M University. [Thesis web-link]

Career after degree: Cummins, Columbus.

MAY 2011 Maruti MUDUNURU

"A framework for coupled deformation-diffusion analysis with application to degradation/healing," Texas A&M University. [Thesis web-link]

Career after degree: Continued with Ph.D. 

DEC 2011 Priyanka GOTIKA

"Non-smooth dynamics using differential-algebraic equations perspective: Modeling and numerical solutions," Texas A&M University. [Thesis web-link]

Career after degree: MathWorks (MATLAB), Boston.

MAY 2013 Justin CHANG

"Modification to Darcy model for high pressure and high velocity applications and associated mixed finite element formulations," University of Houston

Career after degree: Continued with Ph.D. 

 

COURSES TAUGHT 

  • CIVE 2330: Statics (SP17)
  • CIVE 2332: Mechanics of Solids (FA11, SP13, SP14, SP16)
  • CIVE 7336: Finite Element Methods (SP12, SP15, SP17) [Course website]
  • CIVE 7397: Computational Mechanics* (FA12, FA14, FA16) [Course website]
  • CIVE 7397: Mechanics of Porous Media* (FA13, FA15, FA17) [Course website]
  • CIVE 6111: Graduate Seminar Series (FA13)

(* Developed a new graduate-level course.)

COURSES TAUGHT AT OTHER INSTITUTIONS

  • Statics & Particle Dynamics 
  • Engineering Analysis for Mechanical Engineers 
  • Finite Element Method
  • Nonlinear Finite Element Method

SOME TRIVIA

One of my hobbies is to read about history of science (mainly mechanics, physics, thermodynamics and mathematics), biographies of mathematicians and scientists, and trace academic genealogies.

My Erdos number is 4.

P. Erdos ==> J. Pach ==> T.K. Dey ==> A. Hirani ==> K.B. Nakshatrala 

P. Erdos ==> P. Hell ==> J. Kratochvil ==> K.R. Rajagopal ==> K.B. Nakshatrala 

My academic genealogy goes as follows:

Nakshatrala Academic Genealogy

Awards & Honors: 

Teaching Excellence Award, Cullen College of Engineering, 2015.
New Faculty Award, University of Houston, 2012.
TAMU Student-Led Award for Teaching Excellence (SLATE), Texas A&M University, 2009. [Awarded to less than 10 faculty members each semester in the whole college of engineering, Texas A&M University.]
Adviser of Maruti Mudunuru, Best Dissertation Award, Cullen College of Engineering, University of Houston, 2015.

Academic Awards: 

In top 2% (out of over 100,000 students) in the entrance examination for the prestigious Indian Institute of Technology, 1996.
Secured a rank of 197 out of over 100,000 students all over India in Roorkee Entrance Examination, 1996.
Received a merit certificate from the Central Board of Secondary Education (CBSE), India, for being among the top 0.1% in Mathematics nationwide, 1996.

AWARDS TO MY STUDENTS / MY RESEARCH

National/International Level

  • Maruti Mudunuru is the winner of 2016 Melosh Medal, which is given to the best student paper in Computational Mechanics.
  • Maruti MUDUNURU received student travel award from the Haythornthwaite Foundation to attend ASME IMECE 2015 conference. The award is typically given to 10-15 students.
  • Justin CHANG (Ph.D. student) got travel grant from the US Association for Computational Mechanics (USACM) to attend the US National Congress on Computational Mechanics 2015 conference. He won the award based on the abstract: "A comparative study on the computational efficiency of locally conservative finite element methods for subsurface flows," J. Chang, K. B. Nakshatrala, and L. Johnsson. The award consists of $600 and waiver of conference registration fee ($400).
  • Justin CHANG (Ph.D. student of CAML) has been selected to participate in the Argonne Training Program for Extreme-Scale Computing (ATPESC) to be held from August 2-14, 2015 at St. Charles, Illinois. The official selection statement reads: “With around 65 participants accepted each year, admission to the ATPESC program is highly competitive. ATPESC is funded by the U.S. Department of Energy’s Office of Science.” (UH eNews Coverage)
  • Justin CHANG (Ph.D. student) got U.S. Department of Energy Office of Science Graduate Research Award, 2014 - 2015. The title of the research proposal is "Enhancing predictive capability of flow and transport in the subsurface." (UH eNews Coverage)
  • Saeed KARIMI (Ph.D. student) got travel grant from the Society of Industrial and Applied Mathematics to attend 2015 SIAM Conference on Computational Science and Engineering (CSE15) in Salt Lake City. He won the award based on the conference talk abstract, statement of purpose, and reference letter. The tile of his talk is "Monolithic multi-time-step coupling methods for transient systems." The award consists of $650 and waiver of conference registration fee. (College of Engineering Article) (UH eNews Coverage)
  • Maruti MUDUNURU (Ph.D. student) got travel grant from theSociety of Industrial and Applied Mathematics to attend 2013 SIAM Conference on Computational Science and Engineering (CSE13) in Boston. He won the award based on the abstract (and reference letters): "A robust non-negative numerical framework for diffusion-controlled bimolecular-reactive systems." The award consists of $650 and waiver of conference registration fee. (CEE UH News web-link)
  • Maruti MUDUNURU (Ph.D. student) got $500 scholarship from the American Society of Indian Engineers (ASIE), November 2012.
  • The following abstract has been awarded travel grant from the US Association for Computational Mechanics (USACM) to present at the USNCCM 2011 conference: "On the performance of high-order finite element models with respect to maximum principles and the non-negative constraint," G. S. Payette, K. B. Nakshatrala, and J. N. Reddy. The award consisted of $500 and waiver of conference registration fee.
  • Maruti MUDUNURU (Ph.D. student) got travel grant from the US Association for Computational Mechanics (USACM) to attend the USNCCM 2011 conference. He won the award based on the abstract: "A mathematical model and computational framework for degradation / healing of materials and structures," M. K. Mudunuru, and K. B. Nakshatrala. The award consisted of $500 and waiver of conference registration fee.

University/College Level

  • Maruti MUDUNURU got the best dissertation award from the Cullen College of Engineering, 2015. (College of Engineering News Article.)
  • Aisula SALIYEVA (U.G. student at CAML) has been awarded theProvost Undergraduate Research Scholarship (PURS) for FALL 2014. She will generate 2D and 3D finite element meshes of branching arteries w/o aneurysms, which will be used by other CAML researchers to simulate blood flow in deformable arteries.
  • Mohammad ALI (U.G. student at CAML) has been awarded the Summer Undergraduate Research Fellowship (SURF) for 2014.
  • Justin CHANG (Ph.D. student at UH) has been awarded the first year fellowship from the Houston Endowment Fund for 2012-2013.
  • Adolfo ARANZALES (U.G. student at UH) has been awarded the Provost Undergraduate Research Scholarship (PURS) for 2012.
  • Shriram SRINIVASAN (graduate student of CAML at TAMU) got first place in both Aerospace Engineering Session and Taxonomy, 13th Annual Student Research Week, Texas A&M University, 2010.
  • Harsha NAGARAJAN (graduate student of CAML at TAMU) got second place in Taxonomy (Computational Sciences session),13th Annual Student Research Week, Texas A&M University, 2010.

PROFESSIONAL SERVICE

Mini-symposia Organization

  • Transport in heterogeneous porous media, Organizers: K.B. Nakshatrala (Chair), and D.Z. Turner, ASME International Mechanical Engineering Congress and Exposition (IMECE), Vancouver, Canada, November 12-18, 2010.
  • Emerging computational methods for transient non-linear problems with multiple temporal scales, Organizers: G.Hulbert, A. Lew, K.B. Nakshatrala, K.C. Park, A. Prakash (Chair),11th US National Congress on Computational Mechanics, Minneapolis, Minnesota, July 25-28, 2011.
  • Flow and transport in heterogeneous porous media, Organizers: K.B. Nakshatrala (Chair), and D.Z. Turner, 11th US National Congress on Computational Mechanics, Minneapolis, Minnesota, July 25-28, 2011.
  • Flow and transport in heterogeneous porous media, Organizers: K.B. Nakshatrala (Chair), D.Z. Turner, M. Martinez, and S. Karra, ASME International Mechanical Engineering Congress and Exposition (IMECE), Houston, November 9-15, 2012.
  • Environmental effects and fatigue of engineering structures / materials, Organizers: K.B. Nakshatrala (Chair), and K.J. Willam,ASME International Mechanical Engineering Congress and Exposition (IMECE), Houston, November 9-15, 2012.
  • Multifunctional composite materials, Organizers: M. Li (Chair),K.B. Nakshatrala, C. Vipulanandan, and D. Jack, ASME International Mechanical Engineering Congress and Exposition (IMECE), Houston, November 9-15, 2012. 
  • Recent advances in theoretical, numerical and experimental methods in flow and transport in porous media, Organizers: S.Karra (Chair), K.B. Nakshatrala, A. Cortis, and S. Anwar, American Geophysical Union Fall Meeting, San Francisco, December 3-7, 2012.
  • Flow and transport in heterogeneous porous media, Organizers: K.B. Nakshatrala (Chair), D.Z. Turner, M. Martinez, and S. Karra, 12th US National Congress on Computational Mechanics, Raleigh, North Carolina, July 22-25, 2013.
  • Mathematical and numerical modeling of degradation of materials and structures, Organizers: K.B. Nakshatrala (Chair), R. Duddu, J.N. Reddy, and K.J. Willam, 12th US National Congress on Computational Mechanics, Raleigh, North Carolina, July 22-25, 2013.
  • Continuum scale modeling of flow and reactive transport in porous media, Organizers: S. Karra, and K.B. Nakshatrala,American Geophysical Union Fall Meeting, San Francisco, December 9-13, 2013.
  • Continuum scale modeling of flow and reactive transport in porous media, Organizers: S. Karra, and K.B. Nakshatrala,American Geophysical Union Fall Meeting, San Francisco, December 15-19, 2014.
  • Mathematical and numerical modeling of degradation of materials and structures,Organizers: K.B. Nakshatrala (Chair), D.Z. Turner, K.J. Willam and R. Ballarini, 13th US National Congress on Computational Mechanics, San Diego, California, July 26-30, 2015. 
  • Modeling flow and transport in heterogeneous porous media, Organizers: K.B. Nakshatrala (Chair), S. Karra and H. Viswanathan, 13th US National Congress on Computational Mechanics, San Diego, California, July 26-30, 2015. 
  • Advances in forward and inverse modeling of coupled Thermo-Hydro-Geomechanical-Chemical processes in porous media, Organizers: D. Bau, S. Karra, S. Teatini, and K.B. NakshatralaAmerican Geophysical Union Fall Meeting, San Francisco, December 14-18, 2015.

Research Interests: 

Nakshatrala's general research interest includes mathematical formulation and analysis, and development of computational techniques for problems in structural, solid, and fluid mechanics. His current research interests include degradation/healing of man-made and natural materials, and heterogeneous porous media (both flow and structural aspects).

Nakshatrala's application areas include degradation/healing of civil and aerospace structures and materials, geosciences (contaminant transport, carbon-dioxide sequestration, enhanced oil recovery) and bio-mechanics. The research goal is to develop relevant mechanics, numerical techniques, and mathematical tools to model and study various (steady state and transient) multiscale phenomena. Specific research topics of interest include:

Geomechanics

  • Flow and transport in deformable porous media
  • Constitutive modeling of geomaterials (e.g., soil, rock, concrete)
  • Fracturable porous media

Computational Mechanics

  • Multiscale and stabilized finite elements
  • Coupled problems, structure-structure interaction, fluid-structure interaction
  • Numerical homogenization and upscaling techniques
  • Numerical optimization and sensitivity analysis
  • Applications and numerical techniques for differential-algebraic equations (DAEs)

Continuum Physics

  • Modeling degradation / healing of materials and structures
  • Nonlinear continuum mechanics
  • Thermomechanical constitutive modeling & Implicit constitutive modeling
  • Theory of interacting continua

Applied Mathematics and High Performance Computing

  • Partial Differential Equations (More of a spectator)
  • Maximum Principles
  • Applied Optimization
  • Parallel Computing

Invited Presentations / Lectures: 

Rice University, Graduate Seminar, Department of Civil and Environmental Engineering: “Importance of non-negative solutions in degradation modeling, groundwater modeling, and reactive transport,” February 7, 2014.
University of Houston, Graduate Seminar, Department of Civil and Environmental Engineering: "Modeling flow and transport in heterogeneous porous media,” November 16, 2011.
Sandia National Laboratories: “On enforcing maximum principles and the non-negative constraint for diffusion-type equations," April 25, 2011.
University of Houston, Department of Civil and Environmental Engineering: “Mathematical and computational modeling of degradation of materials,” March 7, 2011.
University of Pittsburg, Department of Civil and Environmental Engineering: “A framework for coupled deformation - diffusion analysis with application to degradation / healing,” February 18, 2011.
Rice University, Specialty seminar, Department of Civil and Environmental Engineering: “Modeling flow and transport in heterogeneous porous media,” November 5, 2010.
Columbia University, Department of Civil Engineering and Engineering Mechanics: “Capturing multiple scales for simulation of engineering problems,” April 14, 2008.
Texas A&M University, Department of Mechanical Engineering: “Stabilized finite elements and multiscale formulations,” Department of Mechanical Engineering, March 24, 2008.
University of Illinois at Urbana-Champaign, CSAR/CSE Noon seminars: “Stability of coupling algorithms,” April 6, 2005.

CONFERENCE PRESENTATIONS

2017

  • S.H.S. Joodat*, K.B. Nakshatrala and R. Ballarini, “A computational framework to model flow in porous media with multiple pore-networks," ASCE EMI Conference, San Diego, June 4-7, 2017. [Student poster competition]
  • S.H.S. Joodat*, K.B. Nakshatrala and R. Ballarini, “A framework to model flow in porous media with multiple pore-networks," ASCE EMI Conference, San Diego, June 4-7, 2017. [Conference talk]
  • J. Chang*, K.B. Nakshatrala, M. Knepley and L. Johnsson, “A performance spectrum for parallel computational frameworks for solving PDEs," Firedrake '17 Workshop, Imperial College, London, March 27-28, 2017.

2016

  • J. Chang*, and K.B. Nakshatrala, “Operator-splitting and variational inequalities for non-negative solutions of advection-diffusion equations,” American Geophysical Union (AGU) Fall Meeting, San Francisco, California, December 12-16, 2016.
  • M. Shabouei*, and K.B. Nakshatrala, “Miscible viscous fingering in porous media with multiple pore-networks," American Geophysical Union (AGU) Fall Meeting, San Francisco, California, December 12-16, 2016.
  • M.K. Mudunuru, S. Karra, and K.B. Nakshatrala, "Scaling laws and reduced-order models for mixing and reactive-transport in heterogeneous anisotropic porous media," American Geophysical Union (AGU) Fall Meeting, San Francisco, December 12-16, 2016.
  • S.H.S. Hanie*, K.B. Nakshatrala, and R. Ballarini, “Modeling flow in porous media with double porosity/permeability,” American Geophysical Union (AGU) Fall Meeting, San Francisco, California, December 12-16, 2016.
  • M.K. Mudunuru, K.B. Nakshatrala, and S. Karra, "Preserving physical and mathematical properties under reduced-order modeling for flow and transport in porous media," XXI International Conference Computational Methods in Water Resources (CMWR 2016), University of Toronto, Canada, June 20-24, 2016.
  • M. Shabouei*, and K.B. Nakshatrala, "Effect of temperature and performance of stabilized formulations for viscous fingering and mixing in porous media," EMI Conference, Vanderbilt University, May 22-25, 2016.
  • C. Xu*, and K.B. Nakshatrala, "Degradation of materials and structures due to temperature and moisture: Semi-analytical solutions, computational framework, and numerical solutions," EMI Conference, Vanderbilt University, May 22-25, 2016.
  • S. Karimi*, and K.B. Nakshatrala, "A hybrid multi-scale computational framework for transport problems in porous media," EMI Conference, Vanderbilt University, May 22-26, 2016.
  • J. Chang*, and K.B. Nakshatrala, "Performance model for finite element formulations," The 7th Annual Scientific Software Days Conference, Austin, February 25-26, 2016. [Poster presentation]

2015

  • J. Chang*, and K.B. Nakshatrala, "A new approach to enforce element-wise mass/species balance using the augmented Lagrangian method," American Geophysical Union (AGU) Fall Meeting, December 14-18, 2015. (Poster presentation)
  • M.K. Mudunuru*, S. Shabouei*, and K.B. Nakshatrala, "A locally conservative non-negative finite element formulation for anisotropic advective-diffusive-reactive systems," American Geophysical Union (AGU) Fall Meeting, December 14-18, 2015. (Poster presentation)
  • C. Xu*, and K.B. Nakshatrala, "Chemical degradation of hyperelastic solids: Mathematical model and coupling algorithms," ASME International Mechanical Engineering Congress and Exposition (IMECE), Houston, November 13-19, 2015. (Oral presentation)
  • M.K. Mudunuru*, M. Shabouei*, and K.B. Nakshatrala, "On local and global species conservation errors for nonlinear ecological models and chemical reacting flows," ASME International Mechanical Engineering Congress and Exposition (IMECE), Houston, November 13-19, 2015. (Oral presentation)
  • J. Chang*, S. Karra, and K.B. Nakshatrala, "Enhanced predictive capabilities of large-scale subsurface flow and transport," ASME International Mechanical Engineering Congress and Exposition (IMECE), Houston, November 13-19, 2015. (Oral presentation)
  • M. Shabouei*, and K.B. Nakshatrala, "A posteriori error estimation techniques to verify numerical solutions in porous media models," ASME International Mechanical Engineering Congress and Exposition (IMECE), Houston, November 13-19, 2015. (Oral presentation)
  • J. Chang*, K.B. Nakshatrala, and L. Johnsson, "A comparative study on the computational efficiency of locally conservative finite element methods for subsurface flows," 13th US National Congress on Computational Mechanics (USNCCM), San Diego, July 26-30, 2015. (Student poster competition & Oral presentation)
  • K.B. Nakshatrala, C. Xu*, and M.K. Mudunuru*, "On designing staggered coupling algorithms for modeling degradation of materials," 13th US National Congress on Computational Mechanics (USNCCM), San Diego, July 26-30, 2015. (Oral presentation)
  • J. Chang*, K.B. Nakshatrala, and S. Karra, "Large-scale optimization-based non-negative computational framework for diffusion equations: Parallel implementation and performance studies," PETSc Conference and Tutorial, Argonne National Laboratory, Chicago, June 15-18, 2015.
  • J. Chang*, K.B. Nakshatrala, and L. Johnsson, "A comparative study on the computational efficiency of locally conservative finite element methods for subsurface flows," High Performance Computing in Fluid Flow symposium, The 18th International Conference on Finite Elements in Flow Problems (FEF 2015), Taipei, Taiwan, March 16-18, 2015. (Oral presentation)
  • S. Karimi*, and K.B. Nakshatrala, "Monolithic multi-time-step coupling methods for first and second-order transient systems," SIAM Conference on Computational Science & Engineering (CSE15), March 14-18, 2015. (Poster presentation)
  • S. Karimi*, and K.B. Nakshatrala, "Monolithic multi-time-step coupling methods for transient systems," SIAM Conference on Computational Science & Engineering (CSE15), March 14-18, 2015. (Oral presentation)

2014

  • K.B. Nakshatrala, "On enforcing maximum principles, comparison principles and the non-negative constraint for linear/nonlinear and steady-state/transient diffusion-type equations," AGU Fall Meeting, December 15-19, 2014. (Poster presentation)
  • S. Karimi*, and K.B. Nakshatrala, "A monolithic multi-time-step computational framework for transient advective-diffusive-reactive," AGU Fall Meeting, December 15-19, 2014. (Poster presentation)
  • S. Karra, J. Chang*, and K.B. Nakshatrala, "On the performance of maximum-principle enforcing methods applied to large-scale subsurface problems," AGU Fall Meeting, December 15-19, 2014. (Poster presentation)
  • J. Chang*, and K.B. Nakshatrala, "A methodology to ensure local mass conservation for porous media models under finite element formulations based on convex optimization," AGU Fall Meeting, December 15-19, 2014. (Poster presentation)
  • S. Karimi*, and K.B. Nakshatrala, "Monolithic multi-time-step coupling methods for transient problems in solid mechanics and transport," Experimental and Computational Nonlinear Dynamics session, 51st SES Annual Technical Meeting, Purdue University, October 1-3, 2014. (Oral presentation)
  • S. Karimi*, and K.B. Nakshatrala, "On the development and performance of multi-time-step coupling methods for transient multi-scale problems," Experimental and Computational Nonlinear Dynamics session, 51st SES Annual Technical Meeting, Purdue University, October 1-3, 2014. (Student poster competition)
  • S. Karimi*, and K.B. Nakshatrala, "Monolithic multi-time-step coupling methods for second-order transient systems," 17th US National Congress on Theoretical and Applied Mechanics (USNCTAM), Michigan State University, June 15-20, 2014. (Conference talk and extended abstract)
  • M.K. Mudunuru*, and K.B. Nakshatrala, "On mesh restrictions for mixed formulations for anisotropic diffusion equation in high contrast heterogeneous media," 17th US National Congress on Theoretical and Applied Mechanics (USNCTAM), Michigan State University, June 15-20, 2014. (Conference talk and extended abstract)
  • J. Chang*, and K.B. Nakshatrala, "Computational performance of locally conservative methods for large-scale flow and transport problems through porous media," 17th US National Congress on Theoretical and Applied Mechanics (USNCTAM), Michigan State University, June 15-20, 2014. (Conference talk and extended abstract)

2013

  • K.B. Nakshatrala, "Importance of non-negative numerical solutions in degradation modeling, groundwater modeling, and reactive transport," 12th US National Congress on Computational Mechanics, Raleigh, North Carolina, July 22-25, 2013.
  • M.K. Mudunuru*, C. Xu*, and K.B. Nakshatrala, "On modeling thermal and moisture degradation of materials and structures," 12th US National Congress on Computational Mechanics, Raleigh, North Carolina, July 22-25, 2013. (Oral presentation)
  • M.K. Mudunuru*, and K.B. Nakshatrala, "On mesh restrictions for advective-diffusive-reactive systems to achieve non-negative solutions," 12th US National Congress on Computational Mechanics, Raleigh, North Carolina, July 22-25, 2013. (Student poster competition)
  • M. Martinez, D.Z. Turner, and K.B. Nakshatrala, "A new framework for coupling flow and deformation of the porous solid," 12th US National Congress on Computational Mechanics, Raleigh, North Carolina, July 22-25, 2013. (Oral presentation)
  • J. Chang*, and K.B. Nakshatrala, “On modifications to Darcy model and associated mixed formulations," 12th US National Congress on Computational Mechanics, Raleigh, North Carolina, July 22-25, 2013. (Oral presentation & Student poster competition)
  • S. Karimi*, and K.B. Nakshatrala, “Monolithic vs. staggered coupling algorithms for first- and second-order transient systems," 12th US National Congress on Computational Mechanics, Raleigh, North Carolina, July 22-25, 2013. (Oral presentation)
  • S. Karimi*, and K.B. Nakshatrala, “On multi-time-step coupling for linear first- and second-order transient systems," 12th US National Congress on Computational Mechanics, Raleigh, North Carolina, July 22-25, 2013. (Student poster competition)
  • A.J. Valocchi, and K.B. Nakshatrala,“Importance of non-negative numerical solution for mixing-controlled reactive transport," SIAM Conference on Mathematical & Computational Issues in the Geosciences, University of Padova, Italy, June 17-20, 2013.
  • M.K. Mudunuru*, K.B. Nakshatrala, and A.J. Valocchi, "A robust non-negative numerical framework for diffusion-controlled bimolecular-reactive systems," SIAM Conference on Computational Science and Engineering (SIAM CSE13), Boston, February 25-March 1, 2013.

2012

  • J.N. Reddy, K.B. Nakshatrala, and J. Chang*, “Least-squares finite element formulations for flow problems,” American Geophysical Union (AGU) Fall Meeting, San Francisco, California, December 3-7, 2012. [An invited talk]
  • K.B. Nakshatrala, “Optimization-based methodology for enforcing maximum principles and the non-negative constraint,” American Geophysical Union (AGU) Fall Meeting, San Francisco, California, December 3-7, 2012.
  • M.K. Mudunuru*, and K.B. Nakshatrala, “On achieving element-wise species balance and enforcing non-negative constraint for advection-diffusion equation,” American Geophysical Union (AGU) Fall Meeting, San Francisco, California, December 3-7, 2012.
  • K.B. Nakshatrala, “Numerical modeling of diffusive-reactive systems,” ASME International Mechanical Engineering Congress & Exposition, Houston, Texas, November 9-15, 2012.
  • M.K. Mudunuru*, and K.B. Nakshatrala, “Modeling moisture degradation of structural members,” ASME International Mechanical Engineering Congress & Exposition (Special Session on Environmental effects and failure of engineering structures), Houston, Texas, November 9-15, 2012.

2011

  • K.B. Nakshatrala, “A methodology for enforcing maximum principles and the non-negative constraint for diffusion-type equations ,” 11th US National Congress on Computational Mechanics, Minneapolis, Minnesota, July 25-28, 2011.
  • M.K. Mudunuru*, and K.B. Nakshatrala, “A mathematical model and computational framework for degradation / healing of materials and structures ,” 11th US National Congress on Computational Mechanics, Minneapolis, Minnesota, July 25-28, 2011.
  • G.S. Payette, K.B. Nakshatrala, and J.N. Reddy, “On the performance of high-order finite element models with respect to maximum principles and the non-negative constraint ,” 11th US National Congress on Computational Mechanics, Minneapolis, Minnesota, July 25-28, 2011.

2010

  • D.Z. Turner, P.K. Notz, and K.B. Nakshatrala, “On the performance of Raviart-Thomas and variational multiscale finite element formulations for flow in heterogeneous materials,” ASME International Mechanical Engineering Congress and Exposition, Vancouver, Canada, November 12-18, 2010.
  • K.B. Nakshatrala, “A computational framework for coupled deformation - diffusion analysis,” 16th US National Congress of Theoretical & Applied Mechanics, State College, Pennsylvania, June 27 - July 2, 2010.
  • S. Srinivasan*, and K. B. Nakshatrala, “Stabilized formulations for modified Brinkman equation,” 16th US National Congress of Theoretical & Applied Mechanics, State College, Pennsylvania, June 27 - July 2, 2010.

2009

  • A. J. Valocchi and K. B. Nakshatrala, “Reactions across transverse mixing zones in heterogeneous aquifers: Using effective dispersion coefficients and multi-scale finite element methods,” Reactive Transport and Mixing in Complex Environments: Recent Advances in Theory and Experiments, AGU Fall Meeting, San Francisco, California, December 14 - December 18, 2009.
  • K. B. Nakshatrala, “ Non-negative mixed finite element formulations for tensorial diffusion equation,” Stabilized Methods and Their Applications Session, ASME International Mechanical Congress and Exposition, Lake Buena Vista, Florida, November 13 - 19, 2009.

2008

  • K. B. Nakshatrala, and A.J. Valocchi, “A multiscale finite element framework for reactive contaminant transport in heterogeneous porous media,” Advances in the theory and simulation of flow through porous media Session, ASME International Mechanical Congress and Exposition, Boston, Massachusetts, October 31 - November 6, 2008.
  • K.B. Nakshatrala, and A.J. Valocchi, “On domain decomposition techniques and coupling algorithms for first- and second-order transient systems,” Stabilized and multiscale methods in fluid mechanics Session, ASME International Mechanical Congress and Exposition, Boston, Massachusetts, October 31 - November 6, 2008.
  • D.Z. Turner, K.B. Nakshatrala, and K.D. Hjelmstad, “A Newton-Schur type finite element formulation for Navier-Stokes with applications in nonlinear fluid structure interaction,” 45th Annual Technical Meeting, Society of Engineering Science, Urbana, Illinois, October 12 - 15, 2008.
  • K.B. Nakshatrala, and A.J. Valocchi, “A multiscale finite element framework for simulating reactive contaminant transport in heterogeneous porous media,” Computational Methods in Water Resources, San Francisco, California, July 6-10, 2008.
  • K.B. Nakshatrala, and A.J. Valocchi, “A survey on non-negative numerical formulations for tensorial diffusion equation,” Computational Methods in Water Resources, San Francisco, California, July 6-10, 2008.
  • P.C. Lichtner, C. Lu, G.E. Hammond, B. Philip, J.D. Moulton, R.T. Mills, B.F. Smith, A.J. Valocchi, K. Nakshatrala, S. Yabusaki, "The next-generation massively parallel reactive flow and transport code PFLOTRAN: Application to CO2 storage in saline aquifers," Joint BES-BER-ASCR-FE Research Symposium on Basic Research Relevant to CO2 Sequestration, Gaithersburg, Maryland, March 2008. (Poster session)

2007

  • A.J. Valocchi, and K.B. Nakshatrala, “ Investigation of numerical upscaling techniques for mixing controlled reactions in heterogeneous media,” AGU Fall Meeting, San Francisco, California, December 10-14, 2007.

2006

  • K.B. Nakshatrala, K.D. Hjelmstad, and D.A. Tortorelli, “Partitioned coupling algorithms for multi-physics problems,” 7th World Congress on Computational Mechanics, Los Angeles, California, July 16-22, 2006.

2005

  • A. Namazifard, K. Nakshatrala, B. Wasistho, D. Tortorelli, and K. Hjelmstad, “On some coupling algorithms for fluid-structure interaction problems,” 8th US National Congress on Computational Mechanics, Austin, Texas, July 25-27, 2005.

Peer-Reviewed Journal Articles: 

J. Chang*, and K.B. Nakshatrala,”Variational inequality approach to enforcing the non-negative constraint for advection-diffusion equations," Computer Methods in Applied Mechanics and Engineering, 320: 287-334, 2017. [Journal link] [arXiv link]

J. Chang*, S. Karra, and K.B. Nakshatrala, "Large-scale Optimization-based Non-negative Computational Framework for Diffusion Equations: Parallel Implementation and Performance Studies,” Journal of Scientific Computing, 70: 243-271, 2017. [Journal link] [arXiv link]

M.K. Mudunuru*, and K.B. Nakshatrala, “On mesh restrictions to satisfy comparison principles, maximum principles, and the non-negative constraint: Recent developments and new results," Mechanics of Advanced Materials and Structures24: 556-590, 2017. [Journal link] [arXiv link]

J. Chang*, K.B. Nakshatrala, and J.N. Reddy, ​“Modification to Darcy-Forchheimer model due to pressure-dependent viscosity: Consequences and numerical solutions," accepted in Journal of Porous Media, 20: 263-285, 2017. [Journal link]

C. Xu*, M.K. Mudunuru*, and K.B. Nakshatrala, ​“Material degradation due to moisture and temperature. Part 1: Mathematical model, analysis, and analytical solutions," Continuum Mechanics and Thermodynamics, 28:1847-1885, 2016. [Journal link] [arXiv link

M. Shabouei*, and K.B. Nakshatrala, “Mechanics-based solution verification for porous media models,” Communications in Computational Physics, 20:1127-1162, 2016. [Journal link] [arXiv link]

S. Karimi*, and K.B. Nakshatrala, ​“Do current lattice Boltzmann methods for diffusion-type equations respect the maximum principle and the non-negative constraint?," Communications in Computational Physics, 20:374-404, 2016. [Journal link] [arXiv link]

M.K. Mudunuru*, and K.B. Nakshatrala, ​“On enforcing maximum principles and achieving element-wise species balance for advection-diffusion-reaction equations under the finite element method," Journal of Computational Physics305:448-493, 2016. [Journal link] [arXiv link]

K.B. Nakshatrala, H. Nagarajan, and M. Shabouei*, ​“A numerical methodology for enforcing maximum principles and the non-negative constraint for transient diffusion equations," Communications in Computational Physics19: 53-93, 2016. [Journal link] [arXiv link]

S. Karimi*, and K.B. Nakshatrala, ​“A monolithic multi-time-step computational framework for first-order transient systems with disparate scales," Computer Methods in Applied Mechanics and Engineering283: 419-453, 2015. [Journal link] [arXiv link]

A.N. Hirani, K.B. Nakshatrala, and J.H. Chaudhry, “​Numerical method for Darcy flow derived using Discrete Exterior Calculus," International Journal of Computational Methods in Engineering Science and Mechanics16: 151-169, 2015. [Journal link] [arXiv link]

D.Z. Turner, K.B. Nakshatrala, and M.J. Martinez, ​“Framework for coupling flow and deformation of a porous solid," International Journal of Geomechanics, 10.1061/(ASCE)GM.1943-5622.0000416, 04014076, 2014. [Journal link] [arXiv link]

S. Karimi(s), and K.B. Nakshatrala, ​“On multi-time-step monolithic coupling algorithms for elastodynamics," Journal of Computational Physics273: 671-705, 2014. [Journal link] [arXiv link]

K.B. Nakshatrala, M.K. Mudunuru(s), and A.J. Valocchi, ​“A numerical framework for diffusion-controlled bimolecular-reactive systems to enforce maximum principles and the non-negative constraint," Journal of Computational Physics253: 278-307, 2013. [Journal link] [arXiv link]

K.B. Nakshatrala, and D.Z. Turner, ​“A mixed formulation for a modification to Darcy equation based on Picard linearizarion and numerical solutions to large-scale realistic problems," International Journal for Computational Methods in Engineering Science & Mechanics14: 524-541, 2013. [Journal link]

P.B. Nakshatrala, D.A. Tortorelli, and K.B. Nakshatrala, ​“Nonlinear structural design using multiscale topology optimization: Static formulation," Computer Methods in Applied Mechanics and Engineering261-262: 167-176, 2013. [Journal link]

G.S. Payette, K.B. Nakshatrala, and J.N. Reddy, ​“On the performance of high-order finite elements with respect to maximum principles and the non-negative constraint for diffusion-type equations," International Journal for Numerical Methods in Engineering,  91: 742-771, 2012. [Journal link] [arXiv link]

M.K. Mudunuru(s), and K.B. Nakshatrala, ​“A framework for coupled deformation-diffusion analysis with application to degradation / healing,” International Journal for Numerical Methods in Engineering, 89: 1144-1170, 2012. [Journal link] [arXiv link]

D.Z. Turner, K.B. Nakshatrala, M. Martinez, and P.K. Notz, ​“Modeling subsurface water resource systems involving heterogeneous porous media using the variational multiscale formulation,” Journal of Hydrology428-429: 1-14, 2012. [Journal link] [arXiv link]

D.Z. Turner, K.B. Nakshatrala, and K.D. Hjelmstad, ​“On stabilized formulations for incompressible Navier-Stokes equationsbased on multiscale decomposition formalism,” Mechanics of Advanced Materials and Structures19: 216-232, 2012. [Journal link]

Shriram Srinivasan(s), and K.B. Nakshatrala, “A stabilized mixed formulation for unsteady Brinkman equation based on the method of horizontal lines,” International Journal for Numerical Methods in Fluids68: 642-670, 2012. [Journal link] [arXiv link]

H. Nagarajan(s) and K.B. Nakshatrala, “Enforcing the non-negativity constraint and maximum principles for diffusion with decay on general computational grids,” International Journal for Numerical Methods in Fluids67: 820-847, 2011. [Journal link] [arXiv link]

K.B. Nakshatrala, and K.R. Rajagopal, “A numerical study of fluids with pressure dependent viscosity flowing through a rigid porous medium,” International Journal for Numerical Methods in Fluids67: 342-368, 2011. [Journal link] [arXiv link]

D.Z. Turner, K.B. Nakshatrala, and K.D. Hjelmstad, “A stabilized formulation for the advection-diffusion equation using the Generalized Finite Element Method,” International Journal for Numerical Methods in Fluids66: 64-81, 2011. [Journal link]

K.B. Nakshatrala, and A.J. Valocchi, “Variational structure of the optimal artificial diffusion method for the advection-diffusion equation,” International Journal of Computational Methods7: 1-14, 2010. [Journal link] [arXiv link]

S. Darbha, K.B. Nakshatrala, and K.R. Rajagopal, “On the vibrations of lumped parameter systems governed by differential-algebraic equations,” Journal of the Franklin Institute347: 87-101, 2010. [Journal link] [arXiv link]

D.Z. Turner, K.B. Nakshatrala, and K.D. Hjelmstad, “A variational multiscale Newton-Schur approach for the incompressible Navier-Stokes equations,” International Journal for Numerical Methods in Fluids62: 119-137, 2010. [Journal link] [arXiv link]

K.B. Nakshatrala, A. Prakash, and K.D. Hjelmstad, “On dual-Schur domain decomposition method for linear first-order transient problems,” Journal of Computational Physics228: 7957-7985, 2009. [Journal link] [arXiv link]

K.B. Nakshatrala, and A.J. Valocchi, “Non-negative mixed finite element formulations for a tensorial diffusion equation,” Journal of Computational Physics228: 6726-6752, 2009. [Journal link] [arXiv link]

D.Z. Turner, K.B. Nakshatrala, and K.D. Hjelmstad, “On the stability of bubble functions and a stabilized mixed finite element formulation for the Stokes problem,” International Journal for Numerical Methods in Fluids60: 1291-1314, 2009. [Journal link] [arXiv link]

P.B. Nakshatrala, K.B. Nakshatrala, and D.A. Tortorelli, “A time-staggered partitioned coupling algorithm for transient heat conduction,” International Journal for Numerical Methods in Engineering78: 1387-1406, 2009. [Journal link]

K.B. Nakshatrala, K.D. Hjelmstad, and D.A. Tortorelli, “A FETI-based domain decomposition technique for time dependent first-order systems based on a DAE approach,” International Journal for Numerical Methods in Engineering75: 1385-1415, 2008. [Journal link]

K.B. Nakshatrala, A. Masud, and K.D. Hjelmstad, “On finite element formulations for nearly incompressible linear elasticity,” Computational Mechanics41: 547-561, 2008. [Journal link]

K.B. Nakshatrala, D.Z. Turner, K.D. Hjelmstad, and A. Masud, “A Stabilized mixed finite element method for Darcy flow based on a multiscale decomposition of the solution,” Computer Methods in Applied Mechanics and Engineering195: 4036-4049, 2006. [Journal link]

D.Z. Turner, K.B. Nakshatrala, and K.D. Hjelmstad, “A finite element approach to composite mold design based on Darcy flow with velocity clipping,” Polymer Composites27: 65-70, 2006. [Journal link]

Peer-Reviewed Conference Papers / Extended Abstracts: 

M.K. Mudunuru(s), M. Shabouei(s), and K.B. Nakshatrala, “On local and global species conservation errors for nonlinear ecological models and chemical reacting flows,” Paper number IMECE2015-52760, ASME International Mechanical Engineering Congress & Exposition, 2015. (10 pages) [Conference paper link]

J. Chang(s), and K.B. Nakshatrala, "Computational performance of locally conservative methods for large-scale flow and transport through porous media," abstract number C-06-523, 17th US National Congress of Theoretical and Applied Mechanics, 2014.

M.K. Mudunuru(s), and K.B. Nakshatrala, "On mesh restrictions for mixed formulations for mixed formulations for anisotropic diffusion equation in high contrast heterogeneous media," abstract number C-06-703, 17th US National Congress of Theoretical and Applied Mechanics, 2014.

S. Karimi(s), and K.B. Nakshatrala, "Monolithic multi-time-step coupling methods for second-order transient systems,"  abstract number C-06-840, 17th US National Congress of Theoretical and Applied Mechanics, 2014.

K.B. Nakshatrala, “A computational framework for coupled deformation–diffusion analysis,” Paper number USNCTAM2010-1265, 16th US National Congress of Theoretical & Applied Mechanics, 2010.

S. Srinivasan(s), and K.B. Nakshatrala, “Stabilized formulations for Brinkman equation,” Paper number USNCTAM2010-1037, 16th US National Congress of Theoretical & Applied Mechanics, 2010.

K.B. Nakshatrala, and A.J. Valocchi, “A multiscale finite element framework for reactive contaminant transport in heterogeneous porous media,” Paper number IMECE2008-67395, ASME International Mechanical Engineering Congress & Exposition, 2008.

A. Namazifard, K. Hjelmstad, P. Sofronis, K. Nakshatrala, D. Tortorelli, and R. Fiedler, “Simulations of propellant slumping in the Titan IV SRMU using constitutive models with damage evolution,” Paper number AIAA 2005-3994, 41st AIAA / ASME / SAE / ASEE Joint Propulsion Conference & Exhibit, 10-13 July 2005, Tuscon, Arizona.

Reports / Manuals: 

S. Karimi(*), and K.B. Nakshatrala, ​“A hybrid multi-time-step framework for pore-scale and continuum-scale modeling of solute transport in porous media," e-print available on arXiv. [arXiv link]

K.B. Nakshatrala, H.S.H. Joodat(*), and R. Ballarini, “Modeling flow in porous media with double porosity/permeability: Mathematical model, properties, and analytical solutions," e-print available on arXiv. [arXiv link]

Journal Reviewer: Advances in Water Resources; Applied Mathematical Modeling; ASCE Journal of Engineering Mechanics; ASCE Journal of Structural Engineering; ASME International Mechanical Engineering Congress & Exposition; ASME Journal of Applied Mechanics; ASME Journal of Applied Mechanics Reviews; Biomechanics and Modeling in Mechanobiology; Communications in Computational Physics; Composites Science and Technology; Computer Methods in Applied Mechanics and Engineering; Continuum Mechanics and Thermodynamics; Engineering Computations; Environmental Science & Technology; Finite Elements in Analysis and Design; International Journal for Computational Methods in Engineering Science & Mechanics; International Journal of Engineering Science; International Journal for Multiphase Flow; International Journal for Numerical Methods in Engineering; Journal of Computational and Applied Mathematics; Journal of Computational Physics; Journal of Engineering Materials and Technology; Journal of Mechanics and Physics of Solids; Meccanica; Mechanics Research Communications; Signal Processing.

Proposal Reviewer: National Science Foundation (NSF) panelist: Mechanics of Materials program, 2010 & 2016; National Science Foundation (NSF) ad hoc reviewer: Material Processing and Manufacturing (03/11), Mechanics of Materials (07/11, 09/11); South Africa National Research Foundation (2013, 2016); NCSU Water Resources Research Institute (2015); National Science Foundation HBCU-UP program (2015); Los Alamos Laboratory Directed Research and Development (LDRD)-DR (2016).

News: 

[November 23, 2015] Maruti MUDUNURU got the Cullen's College of Engineering Best Dissertation Award. Congrats Maruti! (Read the news article.)

[July 26-30, 2015] CAML researchers will have a presence at USNCCM 2015, San Diego. Dr. Nakshatrala organizes two mini-symposia at this conference. (Read presentation titles and about the mini-symposia.)

[December 15-19, 2014] CAML researchers attend AGU Fall Meeting, San Francisco. Dr. Nakshatrala organizes a mini-symposium at this conference. (Read presentation titles and about the mini-symposium.)

[June 15-20, 2014] CAML researchers presented their research at the US National Congress on Theoretical and Applied Mechanics (USNCTAM), Michigan State University, 2014.

[June 2, 2014] Aisula Saliyeva (an undergraduate student at CAML) has been awarded the prestigious Provost Undergraduate Research Scholarship (PURS). She will generate 2D and 3D finite element meshes of branching arteries w/o aneurysms, which will used by other CAML researchers to simulate blood flow in deformable arteries. Congrats Aisula! (Read more about the talks and extended abstracts.)

[Summer 2014] Justin Chang will be doing research at Los Alamos National Laboratories (LANL). He will work on an on-going collaborative project between LANL and CAML. He will be implementing in PFloTran, a massively parallel subsurface numerical simulator, the non-negative formulations that the CAML researchers have developed over the years. Justin's mentor at LANL will be Dr. Satish Karra, who is one of the developers of PFloTran.

[April 11, 2014] Mohammad Ali (an undergraduate student at CAML) has been awarded the prestigious Summer Undergraduate Research Fellowship (SURF), University of Houston, 2014. This research is on modeling of degradation of materials. Congrats Mohammed!

[July 22-25, 2013] CAML researchers attend the 12th US National Congress on Computational Mechanics. (Read presentation titles).

[Apr 15, 2013] Maruti Kumar Mudunuru, a Ph.D. student of CAML, received a travel award from the US Association for Computational Mechanics to attend the 12th US National Congress on Computational Mechanics at Raleigh, North Carolina.  The award is based on the following research abstract: "On mesh restrictions for advective-diffusive-reactive systems to achieve non-negative solutions," M.K. Mudunuru, and K.B. Nakshatrala.

[Dec 3-7, 2012] CAML researchers attend AGU Fall Meeting, San Francisco. (Read presentation titles).

[Nov 9-15, 2012] CAML researchers attend ASME International Mechanical Engineering Congress & Exposition Conference. (Read presentation titles).

[Nov 9, 2012] Maruti Kumar Mudunuru, a Ph.D. student of CAML, received a travel award from SIAM to attend 2013 SIAM Conference on Computational Science and Engineering (CSE13). He won the award based on the abstract: "A robust non-negative numerical framework for diffusion-controlled bimolecular-reactive systems," M. K. Mudunuru, K. B. Nakshatrala, and A. J. Valocchi. (Conference web-link) (CEE UH News web-link)

[Jul 25-28, 2011] CAML researchers attend 11th US National Congress on Computational Mechanics Conference. (Read presentation titles).

[Apr 15, 2011] Maruti Kumar Mudunuru, a Ph.D. student of CAML, received a travel award from US Association for Computational Mechanics to attend the 11th US National Congress on Computational Mechanics at Raleigh, North Carolina.