Publications

Poromechanics: 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," Journal of Applied Mechanics, 85: 081009, 2018. [Journal link] [arXiv link]

Vascular-based Thermal Regulation: K. B. Nakshatrala, "Modeling thermal regulation in thin vascular systems: A mathematical analysis," Communications in Computational Physics, 33(4): 1035-1068, 2023.  [Journal link] [arXiv link]

Non-Negative Formulations: 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 Physics, 305:448-493, 2016. [Journal link] [arXiv link] (Melsoh award was given to the student based on the research reported in this paper)

Stabilized Mixed Finite Element Formulations: H. S. H. Joodat*, K. B. Nakshatrala, and R. Ballarini, "Modeling flow in porous media with double porosity/permeability: A stabilized mixed formulation, error analysis, and numerical solutions," Computer Methods in Applied Mechanics and Engineering, 337: 632-676, 2018. [Journal link] [arXiv link]

Seismic Metamaterials: B. Zhang, H. W. Huang*, F. Menq, J. Wang, K. B. Nakshatrala, K. H. Stokoe, and Y.-L. Mo, "Field experimental investigation on broadband vibration mitigation using metamaterial-based barrier-foundation system," Soil Dynamics and Earthquake Engineering, 155: 107167, 2022. [Journal link]

Material Design:  K. B. Nakshatrala, "How to pose material design problems for flow through porous media applications?: Sensitivity of dissipation rate to medium's permeability holds the key," Physics of Fluids, 34: 023103, 2022. [Journal link] [arXiv link]

Material Degradation: 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] 

Time-Stepping Schemes: S. Karimi* and K. B. Nakshatrala, "On multi-time-step monolithic coupling algorithms for elastodynamics," Journal of Computational Physics, 273: 671-705, 2014. [Journal link] [arXiv link] 

Linear Solvers: M. S. Joshaghani*, J. Chang, K. B. Nakshatrala, and M. G. Knepley, "Composable block solvers for the four-field double porosity / permeability model," Journal of Computational Physics, 386: 428-466, 2019. [Journal link] [arXiv link]

High-Performance Computing: J. Chang*, K. B. Nakshatrala, M. G. Knepley, and L. Johnsson, "A performance spectrum for parallel computational frameworks that solve PDEs," Concurrency and Computation: Practice and Experience, 30: e4401, 2018. [Journal link] [arXiv link]

Deep Learning: N. V. Jagtap*, M. K. Mudunuru, and K. B. Nakshatrala, "A deep learning modeling framework to capture mixing patterns in reactive-transport systems," Communications in Computational Physics, 31: 188-223, 2022.  [Journal link] [arXiv link]

2024

[J66] K. B. Nakshatrala, "Dynamic properties of double porosity/permeability model," Journal of Applied Mechanics, 91(6): 061005, 2024 (Paper No: JAM-23-1498).  [Journal link] [arXiv link]

[J65] K. B. Nakshatrala, and K. Adhikari*, "Thermal regulation in thin vascular systems: A sensitivity analysis," Communications in Computational Physics, 35(2): 427-466, 2024. [Journal link] [arXiv link]

2023

[J64] K. B. Nakshatrala, K. Adhikari*, S. R. Kumar, and J. F. Patrick, "Configuration-independent thermal invariants under flow reversal in thin vascular systems," PNAS Nexus, 2(8): pgad266, 2023. [Journal link] [UH eNews Coverage]

[J63] U. Devi, S. R. Kumar, K. B. Nakshatrala, and J. F. Patrick, "A methodology for measuring heat transfer coefficient and self-similarity of thermal regulation in microvascular material systems," International Journal of Heat and Mass Transfer, 217: 124614, 2023.  [Journal link] 

[J62] N. V. Jagtap*, M. K. Mudunuru, and K. B. Nakshatrala, "CoolPINNs: A physics-informed neural network modeling of active cooling in vascular systems," Applied Mathematical Modelling, 122: 265-287, 2023.  [Journal link] [arXiv link]

[J61] S. Turicek, A. D. Snyder, K. B. Nakshatrala, and J. F. Patrick, "Topological effects of 3D-printed copolymer interlayers on toughening and in situ self-healing in laminated fiber-composites," Composites Science and Technology, 240: 110073, 2023. [Journal link]

[J60] K. B. Nakshatrala, "Modeling thermal regulation in thin vascular systems: A mathematical analysis," Communications in Computational Physics, 33(4): 1035-1068, 2023.  [Journal link] [arXiv link]

[J59] N. H. Ramaswamy, B. Joshi, J. Wang, X. Li, F. Y. Menq, X. Shan, K. B. Nakshatrala, K. H. Stokoe,  and Y. L. Mo, "Experimental study of passive seismic vibration isolation by trench-type periodic barrier," Engineering Structures, 276: 115308, 2023.  [Journal link] 

2022

[J58] A. D. Snyder, Z. J. Phillips, J. S. Turicek, C. E. Diesendruck, K. B. Nakshatrala, and J. F. Patrick, "Prolonged in situ self-healing in structural composites via thermo-reversible entanglement," Nature Communications, 13: 6511, 2022. [Journal link] [Editors' highlights]

[J57] M. S. Joshaghani*, and K. B. Nakshatrala, "A modeling framework for coupling plasticity with species diffusion," 32: 83-125, Communications in Computational Physics, 2022. [Journal link] [arXiv link]

[J56] J. Wang, H. W. Huang*, B. Zhang, F.-Y. Menq, K. B. Nakshatrala, Y. L. Mo, and K. H. Stokoe, "Active isolation tests of metamaterial-based barriers and foundation," 260: 114253, Engineering Structures, 2022. [Journal link]

[J55] K. B. Nakshatrala, "How to pose material design problems for flow through porous media applications?: Sensitivity of dissipation rate to medium's permeability holds the key," Physics of Fluids, 34: 023103, 2022. [Journal link] [arXiv link]

[J54] B. Zhang, H. W. Huang*, F. Menq, J. Wang, K. B. Nakshatrala, K. H. Stokoe, and Y. L. Mo, "Field experimental investigation on broadband vibration mitigation using metamaterial-based barrier-foundation system," Soil Dynamics and Earthquake Engineering, 155: 107167, 2022. [Journal link]

[J53] N. V. Jagtap*, M. K. Mudunuru, and K. B. Nakshatrala, "A deep learning modeling framework to capture mixing patterns in reactive-transport systems," Communications in Computational Physics, 31: 188-223, 2022.  [Journal link] [arXiv link]

2021

[J52] T. Phatak*, and K. B. Nakshatrala, "Effect of viscous shearing stresses on optimal material designs for flow of fluids through porous media," Physics of Fluids, 33: 063109, 2021.  [Journal link] [arXiv link]

[J51] U. Devi, R. Pejman,  Z. J. Phillips, P. Zhang, S. Soghrati, K. B. Nakshatrala, A. R. Najafi, K. R. Schab, and J. F. Patrick, "A microvascular-based multifunctional and reconfigurable metamaterial," Advanced Materials Technologies, 6: 2100433, 2021.  [Journal link] [Journal's cover picture]

[J50] T. Phatak*, and K. B. Nakshatrala, "On optimal designs using topology optimization for flow through porous media applications," Transport in Porous Media, 138(2): 401-441, 2021. [Journal link] [arXiv link]

[J49] R. G. Nannapaneni*, K. B. Nakshatrala, D. Stefaniuk, and K. J. Krakowiak, "Discrete lattice modeling of wave propagation in materials with heterogeneous microstructures," ASCE Journal of Engineering Mechanics, 147(10): 04021075, 2021.  [Journal link] 

[J48] K. B. Nakshatrala, "On boundedness and growth of unsteady solutions under the double porosity/permeability model," Transport in Porous Media, 136: 457-470, 2021. [Journal link] [arXiv link] 

[J47] H. W.  Huang*, B. Zhang, J. Wang, F.-Y. Menq, K. B. Nakshatrala, Y. L. Mo, and K. H. Stokoe, "Experimental study on wave isolation performance of periodic barriers," Soil Dynamics and Earthquake Engineering, 144: 106602, 2021.  [Journal link]

2020

[J46] M. Shabouei*, and K. B. Nakshatrala, "On numerical stabilization in modeling double-diffusive viscous fingering," Transport in Porous Media, 132: 39-52, 2020. [Journal link] [arXiv link]

[J45] A. Rezaei, K. B. Nakshatrala, F. Siddiqui, B. Dindoruk, and M. Soliman, "A global sensitivity analysis and reduced-order models for hydraulically-fractured horizontal wells," Computational Geosciences, 24: 995-1029, 2020. [Journal link] [arXiv link]

2019

[J44] K. B. Nakshatrala, and M. S. Joshaghani*, “On interface conditions for flows in coupled free-porous media," Transport in Porous Media, 130: 577-609, 2019. [Journal link] [arXiv link]

[J43] M. S. Joshaghani*, H. S. H. Joodat*, and K. B. Nakshatrala, “A stabilized mixed discontinuous Galerkin formulation for double porosity / permeability model," Computer Methods in Applied Mechanics and Engineering, 352: 508-560, 2019. [Journal link] [arXiv link]

[J42] W. Witarto*, K. B. Nakshatrala, and Y. L. Mo, “Global sensitivity analysis of frequency band gaps in one-dimensional phononic crystals," Mechanics of Materials, 134: 38-53, 2019. [Journal link] [arXiv link]

[J41] M. S. Joshaghani*, J. Chang, K. B. Nakshatrala, and M. G. Knepley, “Composable block solvers for the four-field double porosity / permeability model," Journal of Computational Physics, 386: 428-466, 2019. [Journal link] [arXiv link]

2018

[J40] H. S. H. Joodat*, K. B. Nakshatrala, and R. Ballarini, “Modeling flow in porous media with double porosity/permeability: A stabilized mixed formulation, error analysis, and numerical solutions," Computer Methods in Applied Mechanics and Engineering, 337: 632-676, 2018. [Journal link] [arXiv link]

[J39] 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," Journal of Applied Mechanics, 85: 081009, 2018. [Journal link] [arXiv link]

[J38] N. K. Mapakshi*, J. Chang* and K.  B. Nakshatrala, ​“A scalable variational inequality approach for flow through porous media models with pressure-dependent viscosity," 359: 137-163, Journal of Computational Physics, 2018. [Journal link] [arXiv link]

[J37] J. Chang*, K. B. Nakshatrala, M. G. Knepley, and L. Johnsson,  ​“A performance spectrum for parallel computational frameworks that solve PDEs," 30: e4401, Concurrency and Computation: Practice and Experience, 2018. [Journal link] [arXiv link]

2017

[J36] 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," Computer Methods in Applied Mechanics and Engineering, 323: 98-131, 2017. [Journal link] [arXiv link]

[J35] 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]

[J34] 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]

[J33] 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 Structures, 24: 556-590, 2017. [Journal link] [arXiv link]

[J32] J. Chang*, K. B. Nakshatrala, and J. N. Reddy, ​“Modification to Darcy-Forchheimer model due to pressure-dependent viscosity: Consequences and numerical solutions," Journal of Porous Media, 20: 263-285, 2017. [Journal link]

2016

[J31] 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] 

[J30] 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]

[J29] 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]

[J28] 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 Physics, 305:448-493, 2016. [Journal link] [arXiv link]

[J27] 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 Physics, 19: 53-93, 2016. [Journal link] [arXiv link]

2015

[J26] 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 Engineering, 283: 419-453, 2015. [Journal link] [arXiv link]

[J25] 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 Mechanics, 16: 151-169, 2015. [Journal link] [arXiv link]

2014

[J24] S. Karimi*, and K. B. Nakshatrala, "On multi-time-step monolithic coupling algorithms for elastodynamics," Journal of Computational Physics, 273: 671-705, 2014. [Journal link] [arXiv link] 

[J23] D. Z. Turner, K. B. Nakshatrala, and M. J. Martinez, "Framework for coupling flow and deformation of a porous solid," International Journal of Geomechanics, 2014. [Journal link] [arXiv link] 

2013

[J22] K. B. Nakshatrala, M. K. Mudunuru*, 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 Physics, 253: 278-307, 2013. [Journal link] [arXiv link]

[J21] K. B. Nakshatrala, and D. Z. Turner, "A mixed formulation for a modification to Darcy equation based on Picard linearization and numerical solutions to large-scale realistic problems," International Journal for Computational Methods in Engineering Science & Mechanics, 14: 524-541, 2013. [Journal link] [arXiv link]

[J20] P.  B. Nakshatrala, D. A. Tortorelli, and K. B. Nakshatrala, "Nonlinear structural design using multiscale topology optimization. Part I: Static formulation," Computer Methods in Applied Mechanics and Engineering, 261-262: 167-176, 2013. [Journal link]

2012

[J19] 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]

[J18] 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 Hydrology, 428-429: 1-14, 2012. [Journal link] [arXiv link] 

[J17] M. K. Mudunuru*, 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] 

[J16] D. Z. Turner, K. B. Nakshatrala, and K. D. Hjelmstad, "On stabilized formulations for incompresssible Navier-Stokes equations based on multi-scale decomposition formalism," Mechanics of Advanced Materials and Structures, 19: 216-232, 2012. [Journal link]

[J15] Shriram Srinivasan*, 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 Fluids, 68: 642-670, 2012. [Journal link] [arXiv link]

2011

[J14] H. Nagarajan*, 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 Fluids, 67: 820-847, 2011. [Journal link] [arXiv link]

[J13] 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 Fluids, 67: 342-368, 2011. [Journal link] [arXiv link]

[J12] 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 Fluids, 66: 64-81, 2011. [Journal link]

2010

[J11] K. B. Nakshatrala, and A. J. Valocchi, "Variational structure of the optimal artificial diffusion method for the advection-diffusion equation," International Journal of Computational Methods, 7: 559-572, 2010. [Journal link] [arXiv link]

[J10] 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 Institute, 347: 87-101, 2010. [Journal link] [arXiv link]

[J9] 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 Fluids, 62: 119-137, 2010. [Journal link] [arXiv link]

2009

[J8] K. B. Nakshatrala, A. Prakash, and K. D. Hjelmstad, "On dual Schur domain decomposition method for linear first-order transient problems," Journal of Computational Physics, 228: 7957-7985, 2009. [Journal link] [arXiv link]

[J7] K. B. Nakshatrala, and A. J. Valocchi, "Non-negative mixed finite element formulations for a tensorial diffusion equation," Journal of Computational Physics, 228: 6726-6752, 2009.  [Journal link] [arXiv link]

[J6] 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 Fluids, 60: 1291-1314, 2009. [Journal link] [arXiv link]

[J5] 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 Engineering, 78: 1387-1406, 2009. [Journal link]

2008

[J4] 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 Engineering, 75: 1385-1415, 2008. [Journal link]

[J3] K. B. Nakshatrala, A. Masud, and K. D. Hjelmstad, "On finite element formulations for nearly incompressible linear elasticity," Computational Mechanics, 41: 547-561, 2008. [Journal link]

2006

[J2] K. B. Nakshatrala, D. Z. Turner, A. Masud, and K. D. Hjelmstad, "A stabilized mixed finite element method for Darcy flow based on a multliscale decomposition of the solution," Computer Methods in Applied Mechanics and Engineering, 195: 4036-4049, 2006. [Journal link]

[J1] 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 Composites, 27: 65-70, 2006. [Journal link]

[P9] Y. L. Mo, N. H. Ramaswamy,  P. Shrestha, X. Li, K. B. Nakshatrala, and X. Shan, "Where do we stand on metamaterial-based seismic design of engineering structures," ACCCS: Anniversary Workshop in Commemoration of the 1999 Chi-Chi and 2022 Chihshang Earthquakes, Paper No: PS8-2, pages 134-139, 2023. [Proceedings paper link] (6 pages)

[P8] 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, Paper No: IMECE2015-52760, V009T12A018, 2015. [Proceedings paper link] (10 pages)

[P7] J. Chang*, and K. B. Nakshatrala, "Computational performance of locally conservative methods for large-scale flow and transport through porous media," 17th US National Congress of Theoretical and Applied Mechanics, abstract number C-06-523, 2014.

[P6] M. K. Mudunuru*, and K. B. Nakshatrala, "On mesh restrictions for mixed formulations for mixed formulations for anisotropic diffusion equation in high contrast heterogeneous media," 17th US National Congress of Theoretical and Applied Mechanics, abstract number C-06-703, 2014.

[P5] S. Karimi*, and K. B. Nakshatrala, "Monolithic multi-time-step coupling methods for second-order transient systems," 17th US National Congress of Theoretical and Applied Mechanics, abstract number C-06-840, 2014. 

[P4] K. B. Nakshatrala, "A computational framework for coupled deformation-diffusion analysis," 16th US National Congress of Theoretical and Applied Mechanics, paper number USNCTAM2010-1265, 2010.

[P3] S. Srinivasan*, and K. B. Nakshatrala, "Stabilized formulations for modified Brinkman equation," 16th US National Congress of Theoretical and Applied Mechanics, paper number USNCTAM2010-1037, 2010. 

[P2] K. B. Nakshatrala, and A. J. Valocchi, "A multiscale finite element framework for reactive contaminant transport in heterogeneous porous media," ASME International Mechanical Engineering Congress and Exposition, paper number IMECE2008-67395, 2008. 

[P1] A. Namazifard, K. Hjelmstad, P. Sofronis, K. Nakshatrala, D. Tortorelli, R. Fiedler, "Simulations of propellant slumping in the Titan IV SRMU using constitutive models with damage evolution," 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, paper number AIAA2005-3994, 2005. [Download]

[R1] EdgeAI: How to Use AI to Collect Reliable and Relevant Watershed Data, M. K. Mudunuru, X. Chen, S. Karra, G. Hammond, P. Jiang, K. C. Solander, K. B. Nakshatrala, A. Sun, N. Kumar, R. Versteeg, N. P. Qafoku, A. R. Mangel, J. Stegen, T. D. Scheibe, Technical Report, US Department of Energy, Office of Science, OSTI ID: 1769700, 2021.  [A web-link to the report.]

[R2] Concrete Materials with Ultra-High Damage Resistance and Self-Sensing Capacity for Extended Nuclear Fuel Storage Systems, M. Li, K. B. Nakshatrala, K. J. Willam, and X. Yungping, Technical Report, US Department of Energy, OSTI ID: 1346142, 2017.  [A web-link to the report.]

[R3] N. Maslennikova, P. Milillo, K. B. Nakshatrala, R. Ballarini, A. Stubblefield, and L. Dini, "Importance of ice elasticity in simulating tide-induced grounding line variations along prograde bed slopes," preprint available on EGUsphere, 2024.  [Preprint link]

[R4] K. Adhikari*, J. F. Patrick, and K. B. Nakshatrala, "Effect of temperature-dependent material properties on thermal regulation in microvascular composites," e-print available on arXiv, 2024.  [arXiv link]

[R5] D. Oniz*, Y. L. Mo, and K. B. Nakshatrala, "Shapley values and machine learning to characterize metamaterials for seismic applications," e-print available on arXiv, 2021. [arXiv link]