Parallel Building Blocks for Finite Element Simulations. - Denis Vanderstraeten; Matthew G. Knepley (Parallel CFD, 1997)

Parallel Simulation of Particulate Flows. - Matthew G. Knepley; Vivek Sarin; Ahmed H. Sameh (IRREGULAR, 1998)

Optimizing the Evaluation of Finite Element Matrices. - Robert C. Kirby; Matthew G. Knepley; Anders Logg; L. Ridgway Scott (SIAM J. Sci. Comput., 2005)

PetFMM–A dynamically load-balancing parallel fast multipole library - Felipe A. Cruz; Matthew G. Knepley; Lorena A. Barba (CoRR, 2009)

PetRBF–A parallel O(N) algorithm for radial basis function interpolation - Rio Yokota; Lorena A. Barba; Matthew G. Knepley (CoRR, 2009)

Mesh algorithms for PDE with Sieve I: Mesh distribution. - Matthew G. Knepley; Dmitry A. Karpeev (Sci. Program., 2009)

Biomolecular Electrostatics Simulation by an FMM-based BEM on 512 GPUs - Rio Yokota; Tsuyoshi Hamada; Jaydeep P. Bardhan; Matthew G. Knepley; Lorena A. Barba (CoRR, 2010)

Removing the Barrier to Scalability in Parallel FMM - Matthew G. Knepley (CoRR, 2010)

PetClaw: a scalable parallel nonlinear wave propagation solver for Python. - Amal Alghamdi; Aron J. Ahmadia; David I. Ketcheson; Matthew G. Knepley; Kyle T. Mandli; Lisandro Dalcín (SpringSim (HPC), 2011)

Optimal, scalable forward models for computing gravity anomalies - Dave A. May; Matthew G. Knepley (CoRR, 2011)

Mathematical Analysis of the BIBEE Approximation for Molecular Solvation: Exact Results for Spherical Inclusions - Jaydeep P. Bardhan; Matthew G. Knepley (CoRR, 2011)

Accessible, Extensible, Scalable Tools for Wave Propagation Problems - David I. Ketcheson; Kyle T. Mandli; Aron J. Ahmadia; Amal Alghamdi; Manuel Quezada de Luna; Matteo Parsani; Matthew G. Knepley; Matthew Emmett (CoRR, 2011)

Biomolecular electrostatics using a fast multipole BEM on up to 512 gpus and a billion unknowns. - Rio Yokota; Jaydeep P. Bardhan; Matthew G. Knepley; Lorena A. Barba; Tsuyoshi Hamada (Comput. Phys. Commun., 2011)

Composable Linear Solvers for Multiphysics. - Jed Brown; Matthew G. Knepley; David A. May; Lois Curfman McInnes; Barry Smith 002 (ISPDC, 2012)

Computational science and re-discovery: open-source implementations of ellipsoidal harmonics for problems in potential theory - Jaydeep P. Bardhan; Matthew G. Knepley (CoRR, 2012)

Analytical Nonlocal Electrostatics Using Eigenfunction Expansions of Boundary-Integral Operators - Jaydeep P. Bardhan; Matthew G. Knepley; Peter R. Brune (CoRR, 2012)

Programming Languages for Scientific Computing - Matthew G. Knepley (CoRR, 2012)

PyClaw: Accessible, Extensible, Scalable Tools for Wave Propagation Problems. - David I. Ketcheson; Kyle T. Mandli; Aron J. Ahmadia; Amal Alghamdi; Manuel Quezada de Luna; Matteo Parsani; Matthew G. Knepley; Matthew Emmett (SIAM J. Sci. Comput., 2012)

A Domain Decomposition Approach to Implementing Fault Slip in Finite-Element Models of Quasi-static and Dynamic Crustal Deformation. - Brad T. Aagaard; Matthew G. Knepley; Charles A. Williams (CoRR, 2013)

Achieving High Performance with Unified Residual Evaluation. - Matthew G. Knepley; Jed Brown; Karl Rupp; Barry F. Smith (CoRR, 2013)

Unstructured Geometric Multigrid in Two and Three Dimensions on Complex and Graded Meshes. - Peter R. Brune; Matthew G. Knepley; L. Ridgway Scott (SIAM J. Sci. Comput., 2013)

Finite Element Integration on GPUs. - Matthew G. Knepley; Andy R. Terrel (ACM Trans. Math. Softw., 2013)

Modeling Charge-Sign Asymmetric Solvation Free Energies With Nonlinear Boundary Conditions. - Jaydeep P. Bardhan; Matthew G. Knepley (CoRR, 2014)

Implementation of a multigrid solver on a GPU for Stokes equations with strongly variable viscosity based on Matlab and CUDA. - Liang Zheng; Huai Zhang; Taras V. Gerya; Matthew G. Knepley; David A. Yuen; Yaolin Shi (Int. J. High Perform. Comput. Appl., 2014)

Support for Non-conformal Meshes in PETSc's DMPlex Interface. - Tobin Isaac; Matthew G. Knepley (CoRR, 2015)

Unstructured Overlapping Mesh Distribution in Parallel. - Matthew G. Knepley; Michael Lange 001; Gerard J. Gorman (CoRR, 2015)

Flexible, Scalable Mesh and Data Management using PETSc DMPlex. - Michael Lange 001; Matthew G. Knepley; Gerard J. Gorman (CoRR, 2015)

On The Evolution Of User Support Topics in Computational Science and Engineering Software. - Karl Rupp; Satish Balay; Jed Brown; Matthew G. Knepley; Lois C. McInnes; Barry Smith 002 (CoRR, 2015)

Run-Time Extensibility and Librarization of Simulation Software. - Jed Brown; Matthew G. Knepley; Barry F. Smith (Comput. Sci. Eng., 2015)

Composing Scalable Nonlinear Algebraic Solvers. - Peter R. Brune; Matthew G. Knepley; Barry F. Smith; Xuemin Tu (SIAM Rev., 2015)

Extreme-Scale Multigrid Components within PETSc. - Dave A. May; Patrick Sanan; Karl Rupp; Matthew G. Knepley; Barry F. Smith (PASC, 2016)

A stochastic performance model for pipelined Krylov methods. - Hannah Morgan; Matthew G. Knepley; Patrick Sanan; L. Ridgway Scott (Concurr. Comput. Pract. Exp., 2016)

Anisotropic mesh adaptation in Firedrake with PETSc DMPlex. - Nicolas Barral; Matthew G. Knepley; Michael Lange 001; Matthew D. Piggott; Gerard J. Gorman (CoRR, 2016)

Finite Element Integration with Quadrature on the GPU. - Matthew G. Knepley; Karl Rupp; Andy R. Terrel (CoRR, 2016)

Segmental Refinement: A Multigrid Technique for Data Locality. - Mark F. Adams; Jed Brown; Matthew G. Knepley; Ravi Samtaney (SIAM J. Sci. Comput., 2016)

Efficient Mesh Management in Firedrake Using PETSc DMPlex. - Michael Lange 001; Lawrence Mitchell; Matthew G. Knepley; Gerard J. Gorman (SIAM J. Sci. Comput., 2016)

An Algorithm for Computing Lipschitz Inner Functions in Kolmogorov's Superposition Theorem. - Jonas A. Actor; Matthew G. Knepley (CoRR, 2017)

Landau Collision Integral Solver with Adaptive Mesh Refinement on Emerging Architectures. - Mark F. Adams; Eero Hirvijoki; Matthew G. Knepley; Jed Brown; Tobin Isaac; Richard Tran Mills (SIAM J. Sci. Comput., 2017)

A performance spectrum for parallel computational frameworks that solve PDEs. - Justin Chang 001; K. B. Nakshatrala; Matthew G. Knepley; S. Lennart Johnsson (Concurr. Comput. Pract. Exp., 2018)

A hybridizable discontinuous Galerkin method for two-phase flow in heterogeneous porous media. - Maurice S. Fabien; Matthew G. Knepley; Beatrice M. Riviere (CoRR, 2018)

A high order hybridizable discontinuous Galerkin method for incompressible miscible displacement in heterogeneous media. - Maurice S. Fabien; Matthew G. Knepley; Beatrice M. Riviere (CoRR, 2018)

Comparative Study of Finite Element Methods Using the Time-Accuracy-Size(TAS) Spectrum Analysis. - Justin Chang 001; Maurice S. Fabien; Matthew G. Knepley; Richard Tran Mills (SIAM J. Sci. Comput., 2018)

Composable block solvers for the four-field double porosity/permeability model. - M. S. Joshaghani; Justin Chang 001; K. B. Nakshatrala; Matthew G. Knepley (J. Comput. Phys., 2019)

Manycore Parallel Computing for a Hybridizable Discontinuous Galerkin Nested Multigrid Method. - Maurice S. Fabien; Matthew G. Knepley; Richard Tran Mills; Beatrice M. Riviere (SIAM J. Sci. Comput., 2019)

Families of interior penalty hybridizable discontinuous Galerkin methods for second order elliptic problems. - Maurice S. Fabien; Matthew G. Knepley; Beatrice M. Riviere (J. Num. Math., 2020)

Understanding performance variability in standard and pipelined parallel Krylov solvers. - Hannah Morgan; Patrick Sanan; Matthew G. Knepley; Richard Tran Mills (Int. J. High Perform. Comput. Appl., 2021)

Toward performance-portable PETSc for GPU-based exascale systems. - Richard Tran Mills; Mark F. Adams; Satish Balay; Jed Brown; Alp Dener; Matthew G. Knepley; Scott E. Kruger; Hannah Morgan; Todd S. Munson; Karl Rupp; Barry F. Smith; Stefano Zampini; et al. (Parallel Comput., 2021)

Fully Parallel Mesh I/O Using PETSc DMPlex with an Application to Waveform Modeling. - Vaclav Hapla; Matthew G. Knepley; Michael Afanasiev; Christian Boehm; Martin van Driel; Lion Krischer; Andreas Fichtner (SIAM J. Sci. Comput., 2021)

PCPATCH: Software for the Topological Construction of Multigrid Relaxation Methods. - Patrick E. Farrell; Matthew G. Knepley; Lawrence Mitchell; Florian Wechsung (ACM Trans. Math. Softw., 2021)

Landau collision operator in the CUDA programming model applied to thermal quench plasmas. - Mark F. Adams; Dylan P. Brennan; Matthew G. Knepley; Peng Wang (IPDPS, 2022)

The PETSc Community Is the Infrastructure. - Mark F. Adams; Satish Balay; Oana Marin; Lois Curfman McInnes; Richard Tran Mills; Todd S. Munson; Hong Zhang 006; Junchao Zhang; Jed Brown; Victor Eijkhout; Jacob Faibussowitsch; Matthew G. Knepley; et al. (CoRR, 2022)

Parallel Metric-Based Mesh Adaptation in PETSc using ParMmg. - Joseph G. Wallwork; Matthew G. Knepley; Nicolas Barral; Matthew D. Piggott (CoRR, 2022)

Performance Portable Solid Mechanics via Matrix-Free p-Multigrid. - Jed Brown; Valeria Barra; Natalie Beams; Leila Ghaffari; Matthew G. Knepley; William S. Moses; Rezgar Shakeri; Karen Stengel; Jeremy L. Thompson; Junchao Zhang (CoRR, 2022)

On the order of accuracy for finite difference approximations of partial differential equations using stencil composition. - Abhishek Mishra; David Salac; Matthew G. Knepley (CoRR, 2022)

Tetrahedralization of a Hexahedral Complex. - Aman Timalsina; Matthew G. Knepley (CoRR, 2022)

The PETSc Community as Infrastructure. - Mark F. Adams; Satish Balay; Oana Marin; Lois Curfman McInnes; Richard Tran Mills; Todd S. Munson; Hong Zhang 006; Junchao Zhang; Jed Brown; Victor Eijkhout; Jacob Faibussowitsch; Matthew G. Knepley; et al. (Comput. Sci. Eng., 2022)

Conservative Projection Between Finite Element and Particle Bases. - Joseph V. Pusztay; Matthew G. Knepley; Mark F. Adams (SIAM J. Sci. Comput., 2022)

The PetscSF Scalable Communication Layer. - Junchao Zhang; Jed Brown; Satish Balay; Jacob Faibussowitsch; Matthew G. Knepley; Oana Marin; Richard Tran Mills; Todd S. Munson; Barry F. Smith; Stefano Zampini (IEEE Trans. Parallel Distributed Syst., 2022)

A Numerical Study of Landau Damping with PETSc-PIC. - Daniel S. Finn; Matthew G. Knepley; Joseph V. Pusztay; Mark F. Adams (CoRR, 2023)

PETSc/TAO Developments for Early Exascale Systems. - Richard Tran Mills; Mark F. Adams; Satish Balay; Jed Brown; Jacob Faibussowitsch; Toby Isaac; Matthew G. Knepley; Todd S. Munson; Hansol Suh; Stefano Zampini; Hong Zhang 006; Junchao Zhang (CoRR, 2024)

Efficient N-to-M Checkpointing Algorithm for Finite Element Simulations. - David A. Ham; Vaclav Hapla; Matthew G. Knepley; Lawrence Mitchell; Koki Sagiyama (SIAM J. Sci. Comput., 2024)

PETSc/TAO developments for GPU-based early exascale systems. - Richard Tran Mills; Mark F. Adams; Satish Balay; Jed Brown; Jacob Faibussowitsch; Toby Isaac; Matthew G. Knepley; Todd S. Munson; Hansol Suh; Stefano Zampini; Hong Zhang 006; Junchao Zhang (Int. J. High Perform. Comput. Appl., 2025)

A Performance Portable, Fully Implicit Landau Collision Operator with Batched Linear Solvers. - Mark F. Adams; Peng Wang; Jacob Merson; Kevin Huck; Matthew G. Knepley (SIAM J. Sci. Comput., 2025)

Stencil Composition for Finite Difference Approximations of Partial Differential Equations. - Abhishek Mishra; David Salac; Matthew G. Knepley (SIAM J. Sci. Comput., 2025)

Transformations of Computational Meshes. - Matthew G. Knepley (CoRR, 2025)