296 citations · 1.4k across the 65 of their papers we have counts for
5 papers · 1 filter
Programming Languages for Scientific Computing
Matthew G. Knepley
Scientific computation is a discipline that combines numerical analysis, physical understanding, algorithm development, and structured programming. Several yottacycles per year on…
Analytical Nonlocal Electrostatics Using Eigenfunction Expansions of Boundary-Integral Operators
Jaydeep P. Bardhan, Matthew G. Knepley, Peter R. Brune
In this paper, we present an analytical solution to nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key ste…
A low memory, highly concurrent multigrid algorithm
Mark F. Adams
We examine what is an efficient and scalable nonlinear solver, with low work and memory complexity, for many classes of discretized partial differential equations (PDEs) - matrix-f…
Optimizing the Evaluation of Finite Element Matrices
Robert C. Kirby, Matthew Knepley, Anders Logg +1
Assembling stiffness matrices represents a significant cost in many finite element computations. We address the question of optimizing the evaluation of these matrices. By finding…
Computational science and re-discovery: open-source implementations of ellipsoidal harmonics for problems in potential theory
Jaydeep P. Bardhan, Matthew G. Knepley
We present two open-source (BSD) implementations of ellipsoidal harmonic expansions for solving problems of potential theory using separation of variables. Ellipsoidal harmonics ar…