Efficient out‐of‐GPU memory strategies for solving matrix equation generated by method of moments

Abstract

The numerical solution of the dense linear complex valued system of equations generated by the method of moments (MoMs) generally proceeds by factoring the impedance matrix into LU decomposition. Depending on available hardware resources, the LU algorithm can be executed either on sequential or parallel computers. A straightforward parallel implementation of LU factorisation does not yield a well distributed workload, and therefore it is the computationally most expensive step of the MoMs process, especially when adapting to the GPU technology. Some performance improvement of LU decomposition can be achieved by applying a hybrid approach to the parallel processing model. In this reported work, the problem of accelerating an out-ofcore-like LU solver on a heterogeneous low-cost single GPU/CPU computing platform is addressed. For this, a variable panel-width tuning scheme combined with a hybrid panel-based LU decomposition method is employed, which is something of a novelty in the development of dense linear algebra software. To demonstrate the efficiency of the proposed approach some numerical results are provided.

An Efficient Framework for Analysis of Wire-Grid Shielding Structures over a Broad Frequency Range

“…The CPU sequential procedures for computing the elements of the system matrix have been mapped to parallel GPU platform as described in [20]. To enable the solution of relatively large-size problems with MoM-generated matrix exceeding the amount of memory available on the device, a hybrid out-of-GPU memory CULA-panel-based LU decomposition algorithm have been implemented [21]. The algorithm proceeds iteratively with the following two distinct phases: i) panel factorization, and ii) the update of the trailing submatrix.…”

“…1 explains how the CPU/GPU computations are organized. The interested reader is referred to [20], [21] and [23] for more details. …”

Reflexive periodic solutions of general periodic matrix equations

“…During the last decades, much effort has been devoted to develop numerical methods for solving matrix equations. () Yao et al studied the solutions of the matrix equation AX = B with respect to semi‐tensor product . In Chiang, first by using the Kronecker product, some useful results of the solvability of the Sylvester‐like matrix equation AX + f ( X ) B = C were presented, and then the closed‐form solutions of this matrix equation were provided.…”

An Efficient GPU-Based Out-of-Core LU Solver of Parallel Higher-Order Method of Moments for Solving Airborne Array Problems

“…Compared with a single core, a speedup of 15 can be obtained. In [20], an efficient out-of-GPU memory scheme for solving matrix equations generated by MoM was presented, and it also obtains a good speedup on a single CPU/GPU platform. In [21,22], an out-of-core scheme between RAM and hard-disk drives (HDD) using RWGs and higher-order basis functions (HOBs) was adopted to break the limitation of RAM and improve the capability of parallel MoM to solve larger EM problems.…”