GPU-accelerated scalable solver for banded linear systems

Abstract

Solving a banded linear system efficiently is im portant to many scientific and engineering applications. Current solvers achieve good scalability only on the linear systems that can be partitioned into independent subsystems. In this paper, we present a GPU based, scalable Bi-Conj ugate Gradient Stabilized solver that can be used to solve a wide range of banded linear systems. We utilize a row-oriented matrix decomposition method to divide the banded linear system into several correlated sub linear systems and solve them on multiple GPUs collaboratively. We design a number of GPU and MPI optimizations to speedup inter-GPU and inter-machine communications. We evaluate the solver on Poisson equation and advection diffusion equation as well as several other banded linear systems. The solver achieves a speedup of more than 21 times running from 6 to 192 GPUs on the XSEDE's Keeneland supercomputer and because of small communication overhead, can scale upto 32 GPUs on Amazon EC2 with relatively slow ethernet network.

Analysis of Metal Oxide Varistor Arresters for Protection of Multiconductor Transmission Lines Using Unconditionally-Stable Crank–Nicolson FDTD

“…parameters are time-independent (i.e., we neglect corona effect that results in the time-dependent dynamic capacitance matrix C dyn (t)), the matrix A is fixed and needs to be computed only once. Moreover, on each voltage/current node, two of the three blocks are identity (unitary) matrices I. Consequently, the linear matrix system can be efficiently solved in band-storage form, using a parallelized or GPU CUDA solver whose performance scales with bandwidth (related to the number of wires N w ) and not with matrix dimension [50].…”