119,126 research outputs found
Simple and efficient GPU parallelization of existing H-Matrix accelerated BEM code
In this paper, we demonstrate how GPU-accelerated BEM routines can be used in a simple black-box fashion to accelerate fast boundary element formulations based on Hierarchical Matrices (H-Matrices) with ACA (Adaptive Cross Approximation). In particular, we focus on the expensive evaluation of the discrete weak form of boundary operators associated with the Laplace and the Helmholtz equation in three space dimensions. The method is based on offloading the CPU assembly of elements during the ACA assembly onto a GPU device and to use threading strategies across ACA blocks to create sufficient workload for the GPU. The proposed GPU strategy is designed such that it can be implemented in existing code with minimal changes to the surrounding application structure. This is in particular interesting for existing legacy code that is not from the ground-up designed with GPU computing in mind. Our benchmark study gives realistic impressions of the benefits of GPU-accelerated BEM simulations by using state-of-the-art multi-threaded computations on modern high-performance CPUs as a reference, rather than drawing synthetic comparisons with single-threaded codes. Speed-up plots illustrate that performance gains up to a factor of 5.5 could be realized with GPU computing under these conditions. This refers to a boundary element model with about 4 million unknowns, whose H-Matrix weak form associated with a real-valued (Laplace) boundary operator is set up in only 100 minutes harnessing the two GPUs instead of 9 hours when using the 20 CPU cores at disposal only. The benchmark study is followed by a particularly demanding real-life application, where we compute the scattered high-frequency sound field of a submarine to demonstrate the increase in overall application performance from moving to a GPU-based ACA assembly
High-productivity, high-performance workflow for virus-scale electrostatic simulations with Bempp-Exafmm
Biomolecular electrostatics is key in protein function and the chemical
processes affecting it.Implicit-solvent models expressed by the
Poisson-Boltzmann (PB) equation can provide insights with less computational
power than full atomistic models, making large-system studies -- at the scale
of viruses, for example -- accessible to more researchers. This paper presents
a high-productivity and high-performance computational workflow combining
Exafmm, a fast multipole method (FMM) library, and Bempp, a Galerkin boundary
element method (BEM) package. It integrates an easy-to-use Python interface
with well-optimized computational kernels that are written in compiled
languages. Researchers can run PB simulations interactively via Jupyter
notebooks, enabling faster prototyping and analyzing. We provide results that
showcase the capability of the software, confirm correctness, and evaluate its
performance with problem sizes between 8,000 and 2 million boundary elements. A
study comparing two variants of the boundary integral formulation in regards to
algebraic conditioning showcases the power of this interactive computing
platform to give useful answers with just a few lines of code. As a form of
solution verification, mesh refinement studies with a spherical geometry as
well as with a real biological structure (5PTI) confirm convergence at the
expected rate, for boundary elements. Performance results include
timings, breakdowns, and computational complexity. Exafmm offers evaluation
speeds of just a few seconds for tens of millions of points, and
scaling. This allowed computing the solvation free energy of a
Zika virus, represented by 1.6 million atoms and 10 million boundary elements,
at 80-min runtime on a single compute node (dual 20-core Intel Xeon Gold 6148).
All results in the paper are presented with utmost care for reproducibility.Comment: 14 pages, 6 figure
A Study of Speed of the Boundary Element Method as applied to the Realtime Computational Simulation of Biological Organs
In this work, possibility of simulating biological organs in realtime using
the Boundary Element Method (BEM) is investigated. Biological organs are
assumed to follow linear elastostatic material behavior, and constant boundary
element is the element type used. First, a Graphics Processing Unit (GPU) is
used to speed up the BEM computations to achieve the realtime performance.
Next, instead of the GPU, a computer cluster is used. Results indicate that BEM
is fast enough to provide for realtime graphics if biological organs are
assumed to follow linear elastostatic material behavior. Although the present
work does not conduct any simulation using nonlinear material models, results
from using the linear elastostatic material model imply that it would be
difficult to obtain realtime performance if highly nonlinear material models
that properly characterize biological organs are used. Although the use of BEM
for the simulation of biological organs is not new, the results presented in
the present study are not found elsewhere in the literature.Comment: preprint, draft, 2 tables, 47 references, 7 files, Codes that can
solve three dimensional linear elastostatic problems using constant boundary
elements (of triangular shape) while ignoring body forces are provided as
supplementary files; codes are distributed under the MIT License in three
versions: i) MATLAB version ii) Fortran 90 version (sequential code) iii)
Fortran 90 version (parallel code
Spectral/hp element methods: recent developments, applications, and perspectives
The spectral/hp element method combines the geometric flexibility of the
classical h-type finite element technique with the desirable numerical
properties of spectral methods, employing high-degree piecewise polynomial
basis functions on coarse finite element-type meshes. The spatial approximation
is based upon orthogonal polynomials, such as Legendre or Chebychev
polynomials, modified to accommodate C0-continuous expansions. Computationally
and theoretically, by increasing the polynomial order p, high-precision
solutions and fast convergence can be obtained and, in particular, under
certain regularity assumptions an exponential reduction in approximation error
between numerical and exact solutions can be achieved. This method has now been
applied in many simulation studies of both fundamental and practical
engineering flows. This paper briefly describes the formulation of the
spectral/hp element method and provides an overview of its application to
computational fluid dynamics. In particular, it focuses on the use the
spectral/hp element method in transitional flows and ocean engineering.
Finally, some of the major challenges to be overcome in order to use the
spectral/hp element method in more complex science and engineering applications
are discussed
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