A Highly Accurate Regular Domain Collocation Method for Solving Potential Problems in the Irregular Doubly Connected Domains | Zendy

Zhaoqing Wang | Zendy; Shuchen Li | Zendy; Ping Yang | Zendy; Jian Jiang | Zendy; Tengfei Ma | Zendy

Open Access

A Highly Accurate Regular Domain Collocation Method for Solving Potential Problems in the Irregular Doubly Connected Domains

Author(s) -

Zhaoqing Wang,

Shuchen Li,

Ping Yang,

Jian Jiang,

Tengfei Ma

Publication year - 2014

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2014/397327

Subject(s) - barycentric coordinate system , mathematics , interpolation (computer graphics) , domain (mathematical analysis) , mathematical analysis , collocation method , inverse quadratic interpolation , lagrange polynomial , boundary (topology) , collocation (remote sensing) , cartesian coordinate system , polar coordinate system , discretization , geometry , trilinear interpolation , linear interpolation , computer science , polynomial , frame (networking) , ordinary differential equation , telecommunications , differential equation , machine learning

Embedding the irregular doubly connected domain into an annular regular region, the unknown functions can be approximated by the barycentric Lagrange interpolation in the regular region. A highly accurate regular domain collocation method is proposed for solving potential problems on the irregular doubly connected domain in polar coordinate system. The formulations of regular domain collocation method are constructed by using barycentric Lagrange interpolation collocation method on the regular domain in polar coordinate system. The boundary conditions are discretized by barycentric Lagrange interpolation within the regular domain. An additional method is used to impose the boundary conditions. The least square method can be used to solve the overconstrained equations. The function values of points in the irregular doubly connected domain can be calculated by barycentric Lagrange interpolation within the regular domain. Some numerical examples demonstrate the effectiveness and accuracy of the presented method

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