A scalable H-matrix approach for the solution of boundary integral equations on multi-GPU clusters

In this work, we consider the solution of boundary integral equations by means of a scalable hierarchical matrix approach on clusters equipped with graphics hardware, i.e. graphics processing units (GPUs). To this end, we extend our existing single-GPU hierarchical matrix library hmglib such that it is able to scale on many GPUs and such that it can be coupled to arbitrary application codes. Using a model GPU implementation of a boundary element method (BEM) solver, we are able to achieve more than 67 percent relative parallel speed-up going from 128 to 1024 GPUs for a model geometry test case with 1.5 million unknowns and a real-world geometry test case with almost 1.2 million unknowns. On 1024 GPUs of the cluster Titan, it takes less than 6 minutes to solve the 1.5 million unknowns problem, with 5.7 minutes for the setup phase and 20 seconds for the iterative solver. To the best of the authors' knowledge, we here discuss the first fully GPU-based distributed-memory parallel hierarchical matrix Open Source library using the traditional H-matrix format and adaptive cross approximation with an application to BEM problems

A localised multiscale technique in boundary element method for acoustic wave model

The classical boundary element method (BEM) has emerged as a powerful alternative to the finite element method particularly in cases where better accuracy is required due to problems such as stress concentration or where the domain extends to infinity. In numerical calculation, the BEM has been widely used to solve acoustic problems since BEM offers excellent accuracy due to the discretization only on the structure's boundaries and easy mesh generation. However, BEM has some disadvantages. It suffers from certain drawbacks in terms of computational efficiency. Since most of the BEM leads to a linear system of equations with dense coefficient matrix, this prevents the BEM from being applied to large-scale problems or highresolution mesh. Due to these disadvantages, according to the acknowledged literature, some researchers use hybrid BEM coupling with other methods to improve the computational efficiency or to improve the computational time. This research uses a different technique from the existing hybrid BEM which will improve both the computational efficiency and time. This study highlights that BEM is less accurate for high gradient problem and consumes more computational time. To overcome this problem, a new technique known as multiscale boundary element method (MBEM) is introduced for solving two dimensional acoustic problems. MBEM is introduced in order to reduce the computation time and improve numerical accuracy using the localised multiscale boundary element method (LMBEM) with the help of the FORTRAN language and parallel routine OpenMP. In addition, the truncated Newton method and Newton interpolation are introduced in this multiscale technique. The multiscale technique produces the results faster because of interpolation and accurate initial guess value in a linear system while the mesh refinement for particular elements based on gradient produces more accurate results. Numerical calculation is given to illustrate the efficiency of the proposed method and the solutions have been validated and compared with the BEM. The results show that the MBEM is indeed faster than BEM, with the computational time reduction is almost 33.01%. When the 38 elements are solved using LMBEM, it is more accurate as it gives an average error that is almost similar to a ratio of 38:36 with the 1024 elements using MBEM and BEM. In addition, this research is solving the problem on the boundary. It is suggested that the current study be expanded to solve the problem for the internal nodes of the domain since the internal node value is needed

A parallel library for boundary element discretization of engineering problems

In this paper we present a software for parallel solution of engineering problems based on the boundary element method. The library is written in C++ and utilizes OpenMP and MPI for parallelization in both shared and distributed memory. We give an overview of the structure of the library and present numerical results related to 3D sound-hard scattering in an unbounded domain represented by the boundary value problem for the Helmholtz equation. Scalability results for the assembly of system matrices sparsified by the adaptive cross approximation are also presented.Web of Science14511310