GPU friendly fast Poisson solver for structured power grid network analysis

Abstract

In this paper, we propose a novel simulation algorithm for large scale structured power grid networks. The new method formulates the traditional linear system as a special two-dimension Poisson equation and solves it using an analytical expressions based on FFT technique. The computation complexity of the new algorithm is O(NlgN), which is much smaller than the traditional solver's complexity O(N 1.5 ) for sparse matrices, such as the SuperLU solver and the PCG solver. Also, due to the special formulation, graphic process unit (GPU) can be explored to further speed up the algorithm. Experimental results show that the new algorithm is stable and can achieve 100X speed up on GPU over the widely used SuperLU solver with very little memory footprint.

Fast poisson solvers for thermal analysis

“…Also note that the B i,i formulation in the above equation is different from the well known ones in [9][10]; this is due to the fact that we now have Neumann conditions on the x=0 and x=a surfaces, as opposed to Dirichlet conditions in [9] [10]. It can be verified that the eigenvalues and eigenvectors of G are: …”

“…Let us use the same formation Ax=b as (2)(3), and the same x and y discretization as in (10). Let the z coordinates of cell centers be z 0 , z 1 , …, z Dz-1 .…”

“…This method is built upon prior works: the "two-problem approach" from [6] [13], and the "boundary iteration process" from [10]. The common idea is that, to solve Ax=b where A does not satisfy the conditions of FPS/GFS, we can separate A into two parts:…”

QTBiCGSTAB Algorithm for Large Linear Systemand Parallelized

“…And from equations (6,12,14,15) we would get MQT equals to M, as equation (16) To get better efficiency, in the ideal case, suppose the target division length d should meet the equation (17).…”

“…Now there are some iterative methods proposed [11][12][13][14], which need less memory, solve large and complicated linear equations more efficiently. However, there are some deficiencies of them.…”