Parallel Computation of Acoustic Eigenvalue Problems Using a Polynomial Jacobi-Davidson Method

• Main Authors: Sheng-Hong Lai, 賴聲泓
• Other Authors: Feng-Nan Hwang
• Format: Others
• Language: en_US
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/39081535759260242621

碩士 === 國立中央大學 === 數學研究所 === 98 === The acoustic problems usually happens around us in our daily life when we drive a car, take a bus or take a plane. From the problems of acoustic vibrations with damping, a polynomial eigenvalue problem is obtained by applying the Galerkin finite element method. For particular applications, we are interested in finding some selected low frequency eigenvalues which are located within the interior of the spectrum. The size of the resulting eigenproblem is typically large especially for very fined mesh case so that the parallel polynomial eigensolver is need to deal with such problem. The Jacobi-Davidson method provides a fast and efficient manner for solving the interior eigenvalues for the large sparse polynomial eigenvalue problems. We proposed an Jacobi-Davidson method based on an additive Schwarz framework in parallel implementation and used it to solve the polynomial eigenvalue problem arising from the acoustic. And we showed some parallel performance of the additive Schwarz preconditioned Jacobi-Davidson method by numerical experiments. With help of Krylov-Schwarz algorithm for the correction equation, the efficiency of JD algorithm is greatly improved.