Laplace算子谱的混合基摄动逼近
A Mixed Basis Perturbation Approach to Approximate the Spectrum of Laplace Operator
摘要：
本文提出了一种求解Laplace特征值问题的混合基方法，它把边界看作自由Laplace算子的扰动。该方法通过可以预先计算的通用函数将边界与体积分离，从而有效地将问题的复杂性降低到在表面上的计算。同时检索多个特征值。该方法适用于几个二维几何与Neumann边界条件。
英文摘要：
This paper presents a mixed basis approach for Laplace eigenvalue problems, which treats the boundary as a perturbation of the free Laplace operator. The method separates the boundary from the volume via a generic function that can be pre-calculated and thereby effectively reduces the complexity of the problem to a calculation over the surface. Several eigenvalues are retrieved simultaneously. The method is applied to several 2 dimensional geometries with Neumann boundary conditions.
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