TY - JOUR
T1 - A Fast 3D Poisson Solver of Arbitrary Order Accuracy
AU - Braverman, E.
AU - Israeli, M.
AU - Averbuch, A.
AU - Vozovoi, L.
PY - 1998/7/20
Y1 - 1998/7/20
N2 - We present a direct solver for the Poisson and Laplace equations in a 3D rectangular box. The method is based on the application of the discrete Fourier transform accompanied by a subtraction technique which allows reducing the errors associated with the Gibbs phenomenon and achieving any prescribed rate of convergence. The algorithm requiresO(N3logN) operations, whereNis the number of grid points in each direction. We show that our approach allows accurate treatment of singular cases which arise when the boundary function is discontinuous or incompatible with the differential equation.
AB - We present a direct solver for the Poisson and Laplace equations in a 3D rectangular box. The method is based on the application of the discrete Fourier transform accompanied by a subtraction technique which allows reducing the errors associated with the Gibbs phenomenon and achieving any prescribed rate of convergence. The algorithm requiresO(N3logN) operations, whereNis the number of grid points in each direction. We show that our approach allows accurate treatment of singular cases which arise when the boundary function is discontinuous or incompatible with the differential equation.
KW - 3D Poisson solver for Dirichlet problem
KW - Corner and edge singularities
KW - Fourier method
UR - http://www.scopus.com/inward/record.url?scp=0001212957&partnerID=8YFLogxK
U2 - 10.1006/jcph.1998.6001
DO - 10.1006/jcph.1998.6001
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AN - SCOPUS:0001212957
SN - 0021-9991
VL - 144
SP - 109
EP - 136
JO - Journal of Computational Physics
JF - Journal of Computational Physics
IS - 1
ER -