TY - JOUR
T1 - A Robust and Accurate Solver of Laplace's Equation with General Boundary Conditions on General Domains in the Plane
AU - Rikard Ojala
JO - Journal of Computational Mathematics
VL - 4
SP - 433
EP - 448
PY - 2012
DA - 2012/08
SN - 30
DO - http://doi.org/10.4208/jcm.1201-m3644
UR - https://global-sci.org/intro/article_detail/jcm/8441.html
KW - Laplace's equation, Integral equations, Mixed boundary conditions, Robin boundary conditions.
AB - <p style="text-align: justify;">A robust and general solver for Laplace&#39;s equation on the interior of a simply connected domain in the plane is described and tested. The solver handles general piecewise smooth domains and Dirichlet, Neumann, and Robin boundary conditions. It is based on an integral equation formulation of the problem. Difficulties due to changes in boundary conditions and corners, cusps, or other examples of non-smoothness of the boundary are handled using a recent technique called recursive compressed inverse preconditioning. The result is a rapid and very accurate solver which is general in scope, and its performance is demonstrated via some challenging numerical tests.</p>