High-Performance Computing for Spectral Approximations

P. B. Vasconcelos (), O. Marques () and J. E. Roman ()
Additional contact information
P. B. Vasconcelos: Universidade do Porto
O. Marques: Lawrence Berkeley National Laboratory
J. E. Roman: Universidad Politécnica de Valencia

Chapter 33 in Integral Methods in Science and Engineering, Volume 2, 2010, pp 351-360 from Springer

Abstract: Abstract In this chapter, we focus on the numerical solution of large eigenvalue problems arising in finite-rank discretizations of integral operators. Let X be a Banach space over ℂ and T a compact linear operator defined on X. We aim to solve numerically the eigenvalue problem $$T\varphi = \lambda\varphi,$$ with λ nonzero and ϕ defined in X. Approximations λ m and ϕ m for the spectral elements of the integral operator can be obtained by solving $$T_{m\varphi m} = \theta_{m\varphi m},$$ where (T m ) is a sequence of finite-rank operators converging to T [AhLa01]. By evaluating the projected problem on a specific basis function, it is reduced to a matrix spectral problem 33.1 $$A_m x_m = \theta_m x_m$$ for a finite matrix A m [AhLa06].

Date: 2010
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DOI: 10.1007/978-0-8176-4897-8_33

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