A Fourth-Order Hermitian Box-Scheme with Fast Solver for the Poisson Problem in a Cube

作者：Abbas Ali^*

来源：Numerical Methods for Partial Differential Equations, 2015, 31(3): 609-629.

DOI：10.1002/num.21807

• Hermitian Scheme
• box-scheme
• finite volume method
• high-order compact scheme
• fast solver
• FFT
• Mehrstellenverfahren
• Poisson problem

We present a fourth-order Hermitian box-scheme (HB-scheme) for the Poisson problem in a cube. A single-nonstaggered regular grid is used supporting the discrete unknowns u and delta u. The scheme is fourth-order accurate for u and delta u in L norm. The fast numerical resolution uses a matrix capacitance method, resulting in a computational complexity of O(N3log2(N)). Numerical results are reported on several examples including nonseparable problems. The present scheme is the extension to the three-dimensional case of the HB-scheme presented in Abbas and Croisille [J Sci Comp 49 (2011), 239-267].

• 出版日期2015-5