การพัฒนาระเบียบวิธีการคำนวณสำหรับปัญหาสามมิติแบบเชิงเส้นและเชิงอนุพันธ์อันดับที่สองที่เกี่ยวข้องกับพื้นผิวที่ไม่ต่อเนื่อง ด้วยวิธีการ Weakly Singular Symmetric Galerkin Boundary Element Method (SGBEM)
Development of a computational procedure for three-dimensional, linear, second order, elliptic boundary value problems involving a surface of discontinuity with a weakly singular, symmetric Galerkin boundary element method (SGBEM)
1. To develop a mathematical model in a form of singularity-reduced, weak-form integral equations for a general class of three-dimensional, linear, second order, elliptic, boundary values problems involving a surface of discontinuity. This class of problems includes steady-state Darcy's flow in porous media, elasticity and piezoelectricity problems, and fractures in anisotropic elastic media, piezoelectric media, and piezoelectromagnetic media as special cases. The final set of integral equations is anticipated to contain only weakly singular kernels of order 1/r.
2. To develop a computational model for boundary value problems that involve a surface of discontinuity in unbounded domains. The discretization is based on the weakly singular, symmetric Galerkin boundary element method (SGBEM).
3. To implement a computational model obtained from 2) into an in-house computer code.
4. To generalize the computational model obtained from 2) to treat more general boundary value problems that involve a surface of discontinuity in finite domains.
5. To implement the computational model obtained from 4) into an in-house computer code.
