Effect of Mixed Precision Computing on H-Matrix Vector Multiplication in BEM Analysis

Hierarchical Matrix (H-matrix) is an approximation technique which splits a target dense matrix into multiple submatrices, and where a selected portion of submatrices are low-rank approximated. The technique substantially reduces both time and space complexity of dense matrix vector multiplication, and hence has been applied to numerous practical problems. In this paper, we aim to accelerate the H-matrix vector multiplication by introducing mixed precision computing, where we employ both binary64 (FP64) and binary32 (FP32) arithmetic operations. We propose three methods to introduce mixed precision computing to H-matrix vector multiplication, and then evaluate them in a boundary element method (BEM) analysis. The numerical tests examine the effects of mixed precision computing, particularly on the required simulation time and rate of convergence of the iterative (BiCG-STAB) linear solver. We confirm the effectiveness of the proposed methods.Comment: Accepted manuscript to International Conference on High Performance Computing in Asia-Pacific Region (HPCAsia2020), January 15--17, 2020, Fukuoka, Japa

Status and Future Perspectives for Lattice Gauge Theory Calculations to the Exascale and Beyond

In this and a set of companion whitepapers, the USQCD Collaboration lays out a program of science and computing for lattice gauge theory. These whitepapers describe how calculation using lattice QCD (and other gauge theories) can aid the interpretation of ongoing and upcoming experiments in particle and nuclear physics, as well as inspire new ones.Comment: 44 pages. 1 of USQCD whitepapers

Investigation of general-purpose computing on graphics processing units and its application to the finite element analysis of electromagnetic problems

In this dissertation, the hardware and API architectures of GPUs are investigated, and the corresponding acceleration techniques are applied on the traditional frequency domain finite element method (FEM), the element-level time-domain methods, and the nonlinear discontinuous Galerkin method. First, the assembly and the solution phases of the FEM are parallelized and mapped onto the granular GPU processors. Efficient parallelization strategies for the finite element matrix assembly on a single GPU and on multiple GPUs are proposed. The parallelization strategies for the finite element matrix solution, in conjunction with parallelizable preconditioners are investigated to reduce the total solution time. Second, the element-level dual-field domain decomposition (DFDD-ELD) method is parallelized on GPU. The element-level algorithms treat each finite element as a subdomain, where the elements march the fields in time by exchanging fields and fluxes on the element boundary interfaces with the neighboring elements. The proposed parallelization framework is readily applicable to similar element-level algorithms, where the application to the discontinuous Galerkin time-domain (DGTD) methods show good acceleration results. Third, the element-level parallelization framework is further adapted to the acceleration of nonlinear DGTD algorithm, which has potential applications in the field of optics. The proposed nonlinear DGTD algorithm describes the third-order instantaneous nonlinear effect between the electromagnetic field and the medium permittivity. The Newton-Raphson method is incorporated to reduce the number of nonlinear iterations through its quadratic convergence. Various nonlinear examples are presented to show the different Kerr effects observed through the third-order nonlinearity. With the acceleration using MPI+GPU under large cluster environments, the solution times for the various linear and nonlinear examples are significantly reduced