GPU-based LU decomposition for large method of moments problems

In the method of moments (MOM) analysis of electromagnetic phenomena, the LU decomposition is often an important and costly step in the solution process. In this reported work, the acceleration of LU decomposition using graphics processing units (GPUs) has been considered. Although existing GPU methods, such as those supplied by MAGMA, provide significant speedup over CPU-only implementations, they are limited to smaller problems by the amount of device memory available. The method now presented takes a left-looking LU decomposition as a starting point and uses an out-of-core like approach to significantly increase the size of the problems that can be solved. In addition, a hybrid implementation that utilises MAGMA as part of the solution process is presented, further improving the performance of the method. For the double precision complex variant of the LU decomposition, the number of MOM degrees of freedom that can be solved using a solver based on MAGMA and a GPU device with 1GB of memory is limited to 7936. Using the presented panel-based and hybrid approaches has already permitted problems more than four times larger to be solved with significant speedup.