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Volume 10, Issue 1
Numerical Comparison of the LOOCV-MFS and the MS-CTM for 2D Equations

Fang Hao, Hui Lv & Xiaoyan Liu

DOI: 10.4208/aamm.OA-2016-0184

Adv. Appl. Math. Mech., 10 (2018), pp. 41-61.

Published online: 2018-10

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  • Abstract

The method of fundamental solutions (MFS) and the Collocation Trefftz method have been known as two highly effective boundary-type methods for solving homogeneous equations. Despite many attractive features of these two methods, they also experience different aspects of difficulties. Recent advances in the selection of source location of the MFS and the techniques in reducing the condition number of the Trefftz method have made significant improvement in the performance of these two methods which have been proven to be theoretically equivalent. In this paper we will compare the numerical performance of these two methods under various smoothness of the boundary and boundary conditions.

  • Keywords

Trefftz method, the method of fundamental solution, LOOCV, multiple scale method, non-harmonic boundary conditions.

  • AMS Subject Headings

65M10, 78A48

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-10-41, author = {Hao , FangLv , Hui and Liu , Xiaoyan}, title = {Numerical Comparison of the LOOCV-MFS and the MS-CTM for 2D Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {10}, number = {1}, pages = {41--61}, abstract = {

The method of fundamental solutions (MFS) and the Collocation Trefftz method have been known as two highly effective boundary-type methods for solving homogeneous equations. Despite many attractive features of these two methods, they also experience different aspects of difficulties. Recent advances in the selection of source location of the MFS and the techniques in reducing the condition number of the Trefftz method have made significant improvement in the performance of these two methods which have been proven to be theoretically equivalent. In this paper we will compare the numerical performance of these two methods under various smoothness of the boundary and boundary conditions.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2016-0184}, url = {http://global-sci.org/intro/article_detail/aamm/10500.html} }
TY - JOUR T1 - Numerical Comparison of the LOOCV-MFS and the MS-CTM for 2D Equations AU - Hao , Fang AU - Lv , Hui AU - Liu , Xiaoyan JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 41 EP - 61 PY - 2018 DA - 2018/10 SN - 10 DO - http://doi.org/10.4208/aamm.OA-2016-0184 UR - https://global-sci.org/intro/article_detail/aamm/10500.html KW - Trefftz method, the method of fundamental solution, LOOCV, multiple scale method, non-harmonic boundary conditions. AB -

The method of fundamental solutions (MFS) and the Collocation Trefftz method have been known as two highly effective boundary-type methods for solving homogeneous equations. Despite many attractive features of these two methods, they also experience different aspects of difficulties. Recent advances in the selection of source location of the MFS and the techniques in reducing the condition number of the Trefftz method have made significant improvement in the performance of these two methods which have been proven to be theoretically equivalent. In this paper we will compare the numerical performance of these two methods under various smoothness of the boundary and boundary conditions.

Fang Hao, Hui Lv & Xiaoyan Liu. (2020). Numerical Comparison of the LOOCV-MFS and the MS-CTM for 2D Equations. Advances in Applied Mathematics and Mechanics. 10 (1). 41-61. doi:10.4208/aamm.OA-2016-0184
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