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- A boundary integral Trefftz formulation with symmetric collocation
- Trefftz and Collocation Methods
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Authors : Z-C. Hu, Tunghai University, Taiwan and A. Different from the Finite Element and the Finite Difference methods, the discretization and approximation of the collocation method is based on a set of unstructured points in space.
This text discusses several types of collocation methods including the radial basis function method, the Trefftz method, and the coupled collocation and finite element method. Governing equations investigated include Laplace, Poisson, Helmholtz and biharmonic equations. Regular boundary value problems, boundary value problems with singularity, and Eigenvalue problems are also examined.
Rigorous mathematical proofs are contained in these chapters, and many numerical experiments are also provided to support the algorithms and to verify the theory. A tutorial on the applications of these methods is also provided.
A boundary integral Trefftz formulation with symmetric collocation
In this paper we develop a novel method for the solution of a singularly perturbed convection—diffusion equation by inserting the adjoint Trefftz functions as Full Text Analysis on the method of fundamental solutions for biharmonic equations. S and Tian, Zhaolu. In this paper, the error and stability analysis of the method of fundamental solution MFS is explored for biharmonic equations. The bounds of errors are Full Text The generalized finite difference method for the inverse Cauchy problem in two-dimensional isotropic linear elasticity.
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- Trefftz, collocation, and other boundary methods—A comparison;
In this study, the generalized finite difference method GFDM was used to stably and accurately solve two-dimensional 2D inverse Cauchy problems in linear Full Text A novel space—time meshless method for solving the backward heat conduction problem. This paper presents a novel space—time meshless method for solving the backward heat conduction problem BHCP.
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A numerical approximation is obtained using the Full Text Trefftz, collocation, and other boundary methods—A comparison. We also review the coupling Full Text Fast-multipole accelerated regularized meshless method for large-scale isotropic heat conduction problems.
Trefftz and Collocation Methods
The regularized meshless method RMM belongs to the family of meshless boundary collocation methods and can be viewed as one kind of modified method of The Wave Based Method is a deterministic prediction technique to solve steady-state dynamic problems and is developed to overcome some of the frequency Full Text Many names of the Trefftz method. Moreover, the error analysis is briefly addressed, and new numerical results are reported. Comparisons among TMs and other numerical methods are made.
It is concluded that the CTM is the simplest algorithm, and provides the most accurate solution with the best numerical stability. In this talk we also use the Trefftz method to solve Stokes flow problems.