Coupling Interface Method for Solving Poisson-Boltzmann Equation
Professor Yu-Chen Shu
Department of Mathematics, National Cheng Kung University, Taiwan
In this talk, a coupling interface method (CIM) is proposed
for solving complex interface problems, especially for
Poisson-Boltzmann Equation. The coefficients, the source terms, and
the solutions may be discontinuous or singular across the interfaces.
The method uses adaptive-order strategy and is extended to high
dimensions through a dimension-by-dimension approach. To connect
information from each dimension, a coupled equation for the principal
derivatives is derived through the jump conditions in each coordinate
direction. The cross derivatives are approximated by one-side
interpolation. The method is easy to implement and flexible to
integrate with other approaches. We compare our method with some
existing methods. Numerical tests are carefully performed to show the
efficiency, robustness and accuracy of our method.