Preconditioning for Mimetic Spectral Element Method

Liu, Z.

Preconditioning for Mimetic Spectral Element Method

A Preliminary Study Applied on Elliptic Equations

Master thesis (2018)

Authors

Z. Liu Aerospace Engineering

Contributors

MI Gerritsma (mentor)

Faculty

Aerospace Engineering, Aerospace Engineering

Preconditioning Spectral analysis Mimetic spectral element methods Mimetic discretization

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Published Date

18-12-2018

Language

English

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Faculty

Aerospace Engineering

Abstract

In order to solve linear system of equations obtained from numerical discretisation fast and accurate, preconditioning on the coefficient matrix is needed. In this thesis research, a preliminary study on preconditioning techniques suitable for Mimetic Spectral Element Method (MSEM) will be presented. The spectral limit change of some important discrete operators that appear in MSEM are studied, with respect to the discretisation order change. Some of the limits are proven by theorems and some are estimated by reasoning. Preconditioners and preconditioning techniques are developed and performed on a Poisson problem using both p-version and hp-version MSEM. Lastly in conclusion, the cause of ill-conditioning of MSEM-related systems are discussed; a common framework of preconditioning study for MSEM is proposed, which will be helpful for future studies and application on different problem types.

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