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Multigrid methods for fractional diffusion equations

Trotti, Ken ; Krause, Rolf (Dir.) ; Donatelli, Marco (Codir.)

Thèse de doctorat : Università della Svizzera italiana, 2021 ; 2021INFO013.

Recent years have seen the rapid growth in interest towards fractional calculus. Fractional calculus plays an important role in modelling anomalous diffusion phenomena, however closed-form analytical solutions of such equations are rarely available, hence numerical estimates are needed. In this thesis we consider various fractional diffusion equations (FDEs), where different fractional ...

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Multilevel solution strategies for unfitted finite element methods

Kothari, Hardik ; Krause, Rolf (Dir.)

Thèse de doctorat : Università della Svizzera italiana, 2020 ; 2020INFO009.

In the unfitted finite element methods, traditionally we can use Nitsche's method or the method of Lagrange multipliers to enforce the boundary/interface conditions. In this work, we present tailored multilevel methods for solving the problems stemming from either of these discretizations. Generally, multigrid methods require a hierarchy of finite element (FE) spaces which can be created...

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