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High-Performance Computing for Spectral Approximations

In: Integral Methods in Science and Engineering, Volume 2

Author

Listed:
  • P. B. Vasconcelos

    (Universidade do Porto)

  • O. Marques

    (Lawrence Berkeley National Laboratory)

  • J. E. Roman

    (Universidad Politécnica de Valencia)

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].

Suggested Citation

  • P. B. Vasconcelos & O. Marques & J. E. Roman, 2010. "High-Performance Computing for Spectral Approximations," Springer Books, in: Christian Constanda & M.E. Pérez (ed.), Integral Methods in Science and Engineering, Volume 2, chapter 33, pages 351-360, Springer.
    • Handle: RePEc:spr:sprchp:978-0-8176-4897-8_33
    DOI: 10.1007/978-0-8176-4897-8_33
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