A novel Trefftz method of the inverse Cauchy problem for 3D modified Helmholtz equation

作者：Liu, Chein-Shan; Qu, Wenzhen^*; Chen, Wen; Lin, Ji

来源：Inverse Problems in Science and Engineering, 2017, 25(9): 1278-1298.

DOI：10.1080/17415977.2016.1247449

• Inverse Cauchy problem
• Trefftz method
• three-dimensional modified Helmholtz equation
• multiple
• scale
• direction Trefftz method

We solve an overspecified as well as underspecified inverse Cauchy problems of the modified Helmholtz equation in an arbitrary 3D-bounded domain with a smooth boundary using a multiple/scale/direction Trefftz method (MSDTM), of which the directions are uniformly distributed on S-1, and the scales are determined a priori by the collocation points on boundary to satisfy the specified boundary conditions. The three-dimensional numerical examples confirm the efficiency of theMSDTM. Although under a large noise up to 30%, the solutions of inverse Cauchy problems are quite accurate. More importantly, the present method converges very fast and saves much CPU time.

• 出版日期2017
• 单位山东理工大学; 河海大学