A parallel space–time boundary element method for the heat equation

Semi-analytic integration for a parallel space-time boundary element method modeling the heat equation

“…Indeed, in addition to the evaluation of the distance between spatial coordinates x − y , which is the most time consuming part of the BEM assembly for the Laplace equation, one has to evaluate the exponential and error functions in many quadrature points for all blocks of the Toeplitz matrix. The implementation strategy in shared memory thus follows the ideas presented by the authors previously for 3d space and 2d space-time BEM in [20,21,22]. To make use of modern multicore processors with vector arithmetic units we make use of features of modern OpenMP [23], namely threading and SIMD vectorisation.…”

“…To exploit the full potential of floating point units we vectorise the code at the level of local contributions to the global matrix. For simplicity we opt for the OpenMP implementation of vector processing similarly as in [20,21,22].…”

“…, to ensure unit strided access to data. Earlier work [20,21,22] has shown that this approach is more efficient than an array of vectors.…”

A parallel fast multipole method for a space-time boundary element method for the heat equation

“…Many publications have been devoted to the efficient implementation and parallelization of the FMM (see, e.g., [14,15,16,17,18,19]) mainly for particle simulations, but also for the solution of classical spatial boundary integral equations [20,21], and, less frequently, space-time boundary integral equations [22]. A parallelization of a standard Galerkin space-time BEM for the heat equation in two spatial dimensions was considered in [23].…”