Solving 3D Biharmonic Equation Interior Problem by Using Multiple Scale/Direction Trefftz Method

In this thesis, we develope a multi-scale and multi-directional Trefffz Method numerical method for three-dimensional biharmonic equation Cauchy problem and the inverse problem. In the past, the two-dimensional biharmonic equation has arisen many numerical methods, however, there is still not an efficient numerical method to solve the three-dimensional problem.Here we use Trefftz method for solving the two-dimensional problem and extend this method to solve the problem the three-dimensional.The proposed approach is even moreeffective and simple than the conventient boundary type meshless method. Inverse problem Cauchy problem has a highly morbid, we propose a new post-processing (post-condition) linear system problems to overcome the height of the sick.Then, in the second half of this thesis are respectively two and three dimensional numerical examples, in these examples we use the Dirichlet boundary conditions and Neumann boundary conditions, after which collocation method for solving direct problem and Cauchy inverse problem, and use Matlab programming language and Mathematica software to numerical analysis and simulation.