The application of VLSI Poisson solvers to the biharmonic problem (Q1185910)

The paper is concerned with VLSI designs of parallel algorithms for solving the biharmonic Dirichlet boundary value problem on a square domain. The linear system resulting from the canonical finite difference discretization is treated by an iterative procedure which essentially requires the solution of two discrete Poisson problems in each iteration step. Two direct Poisson solvers are proposed alternatively: a spectral matrix decomposition method and the cyclic odd-even reduction. Both may easily be parallelized. VLSI designs are presented for the Poisson solvers as well as for the total biharmonic problem solver, and the area-time complexity of the algorithms is estimated.