A GPU-Accelerated Linear Solver for Massively Parallel Underground Simulations

Modern engineering applications require the solution of linear systems of millions or even billions of equations. The solution of the linear system takes most of the simulation for large scale simulations, and represent the bottleneck in developing scientific and technical software. Usually, preconditioned iterative solvers are preferred because of their low memory requirements and they can have a high level of parallelism. Approximate inverses have been proven to be robust and effective preconditioners in several contexts. In this communication, we present an adaptive Factorized Sparse Approximate Inverse (FSAI) preconditioner with a very high level of parallelism in both set-up and application. Its inherent parallelism makes FSAI an ideal candidate for a GPU-accelerated implementation, even if taking advantage of this hardware is not a trivial task, especially in the set-up stage. An extensive numerical experimentation has been performed on industrial underground applications. It is shown that the proposed approach outperforms more traditional preconditioners in challenging underground simulation, greatly reducing time-to-solution.

Fast Preconditioner Computation for BICGSTAB-FFT Method of Moments with NURBS in Large Multilayer Structures

Fast computation of the coefficients of the reduced impedance matrix of the method of moment (MM) is proposed by expanding the basis functions (BFs) in pulses and solving an equivalent periodic problem (EPP) for analyzing large multilayer structures with non-uniform rational basis spline (NURBS) modeling of the embedded layout. These coefficients are required by the computation of sparse approximate inverse (SAI) preconditioner, which leads an efficient iterative version of the MM. This reduced coefficient matrix only considers the near field part of the MM matrix. Discrete functions of small sizes are required to implement the pulse expansion and EPP. These discrete functions of small size lead to discrete cyclic convolutions that are computed in a very fast way by fast Fourier transform (FFT)-accelerated matrix–vector multiplication. Results obtained using a conventional laptop show an analysis of very large multilayer structures with resonant layouts, as whole reflectarrays of electrical size 40 times the vacuum wavelengths, where the iterative MM with a SAI preconditioner can be 22.7 times faster than the pure iterative MM without any preconditioner.