5 papers
Fast Evaluation of Derivatives of Green's Functions Using Recurrences
Hirish Chandrasekaran, Andreas Kloeckner
High-order derivatives of Green's functions are a key ingredient in Taylor-based fast multipole methods, Barnes-Hut -body algorithms, and quadrature by expansion (QBX). In these…
Canonicalization of Batched Einstein Summations for Tuning Retrieval
Kaushik Kulkarni, Andreas Klöckner
We present an algorithm for normalizing \emph{Batched Einstein Summation} expressions by mapping mathematically equivalent formulations to a unique normal form. Batches of einsums…
MIRGE: An Array-Based Computational Framework for Scientific Computing
Matthias Diener, Matthew J. Smith, Michael T. Campbell +6
MIRGE is a computational approach for scientific computing based on NumPy-like array computation, but using lazy evaluation to recast computation as data-flow graphs, where nodes r…
A Fast Direct Solver for Boundary Integral Equations Using Quadrature By Expansion
Alexandru Fikl, Andreas Klöckner
We construct and analyze a hierarchical direct solver for linear systems arising from the discretization of boundary integral equations using the Quadrature by Expansion (QBX) meth…
Code Generation for Near-Roofline Finite Element Actions on GPUs from Symbolic Variational Forms
Kaushik Kulkarni, Andreas Klöckner
We present a novel parallelization strategy for evaluating Finite Element Method (FEM) variational forms on GPUs, focusing on those that are expressible through the Unified Form La…