Trefftz spectral method for initial-boundary problems - Lifits, Sergei; Reutskiy, Sergei; Tirozzi, Brunello (Computer Assisted Methods in Engineering and Science, 1997)
We describe a new Quasi Trefftz-type Spectral Method (QTSM) for solving boundary value and initial value problems. QTSM combines the properties of the Trefftz method with the spectral approach. The special feature of QTSM is that we use trial functions which satisfy the corresponding homogeneous equation only approximately. These trial functions are represented in the terms of a truncated series of eigenfunctions of some eigenvalue problem associated with the problem considered. The method has been found to work well for different elliptic problems with the Laplace, the Helmholtz and the biharmonic operators. We also consider some nonstationary parabolic problems including the problem in the domain with moving boundaries. The possibilities of further development of QTSM are also discussed.