TY - JOUR
T1 - Local MFS Matrix Decomposition Algorithms for Elliptic BVPs in Annuli
AU - Chen , C.S.
AU - Karageorghis , Andreas
AU - Lei , Min
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 93
EP - 120
PY - 2024
DA - 2024/02
SN - 17
DO - http://doi.org/10.4208/nmtma.OA-2023-0045
UR - https://global-sci.org/intro/article_detail/nmtma/22912.html
KW - Local method of fundamental solutions, Poisson equation, biharmonic equation, matrix decomposition algorithms, fast Fourier transforms.
AB - <p style="text-align: justify;">We apply the local method of fundamental solutions (LMFS) to boundary
value problems (BVPs) for the Laplace and homogeneous biharmonic equations in
annuli. By appropriately choosing the collocation points, the LMFS discretization
yields sparse block circulant system matrices. As a result, matrix decomposition
algorithms (MDAs) and fast Fourier transforms (FFTs) can be used for the solution
of the systems resulting in considerable savings in both computational time and
storage requirements. The accuracy of the method and its ability to solve large scale
problems are demonstrated by applying it to several numerical experiments.</p>