계산수학 세미나 안내
연사 : 이창옥 교수 (KAIST 수리과학과)
제목 : "Higher-Order, Cartesian Grid Based Finite Difference
Schemes for Elliptic Equations on Irregular Domains"
일시 : 2007년 3월 12일(월) 15:30
장소 : 수리과학과 산업경영동 세미나실(2222호)
Abstract : Second and fourth order Cartesian grid based finite
difference methods are proposed for elliptic and parabolic
partial differential equations, and associated eigenvalue
problems on irregular domains with general boundary
conditions. The methods are based on the continuation of a
solution idea using multivariable Taylor's expansion of the
solution about selected boundary points, and the core ideas
of the immersed interface method. The methods offer
systematic treatment of the general boundary conditions in
two- and three-dimensional domains and are directly applied
to semi-discretize heat equations on irregular domains.
Convergence analysis and numerical examples are
presented. The validity and effectiveness of the proposed
methods are demonstrated through our numerical results
including computations of the eigenvalues of the associated
eigenvalue problem.