A fourth‐order Hermitian box‐scheme with fast solver for the Poisson problem in a cube |
| |
Authors: | Ali Abbas |
| |
Institution: | Department of Mathematics, Faculty of Sciences, Lebanese International University, Bekaa‐Rayak, Lebanon |
| |
Abstract: | 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 . The scheme is fourth‐order accurate for u and in norm. The fast numerical resolution uses a matrix capacitance method, resulting in a computational complexity of . 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]. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 609–629, 2015 |
| |
Keywords: | Hermitian Scheme box‐scheme finite volume method high‐order compact scheme fast solver FFT Mehrstellenverfahren Poisson problem |
|
|