Publication

Multilevel preconditioners for elliptic problems with multiple scales

Publications associées (113)

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Total Flow Analysis (TFA) is a method for the worst-case analysis of time-sensitive networks. It uses service curve characterizations of the network nodes and arrival curves of flows at their sources; for tractability, the latter are often taken to be line ...

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Spectral Coarse Spaces for the Substructured Parallel Schwarz Method

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The parallel Schwarz method (PSM) is an overlapping domain decomposition (DD) method to solve partial differential equations (PDEs). Similarly to classical nonoverlapping DD methods, the PSM admits a substructured formulation, that is, it can be formulated ...

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A local adaptive discontinuous Galerkin method for convection-diffusion-reaction equations

Assyr Abdulle, Giacomo Rosilho De Souza

We introduce a local adaptive discontinuous Galerkin method for convection-diffusion-reaction equations. The proposed method is based on a coarse grid and iteratively improves the solution's accuracy by solving local elliptic problems in refined subdomains ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

On the nonlinear Dirichlet-Neumann method and preconditioner for Newton's method

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Springer-Verlag2021

Efficient algorithms for wave problems

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Wave phenomena manifest in nature as electromagnetic waves, acoustic waves, and gravitational waves among others.Their descriptions as partial differential equations in electromagnetics, acoustics, and fluid dynamics are ubiquitous in science and engineeri ...

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Complexity analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

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We consider the numerical approximation of an optimal control problem for an elliptic Partial Differential Equation (PDE) with random coefficients. Specifically, the control function is a deterministic, distributed forcing term that minimizes the expected ...

2021

Substructured Two-grid and Multi-grid Domain Decomposition Methods

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Two-level domain decomposition methods are very powerful techniques for the efficient numerical solution of partial differential equations (PDEs). A two-level domain decomposition method requires two main components: a one-level preconditioner (or its corr ...

2021

On the asymptotic optimality of spectral coarse spaces

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This paper is concerned with the asymptotic optimality of spectral coarse spaces for two-level iterative methods. Spectral coarse spaces, namely coarse spaces obtained as the span of the slowest modes of the used one-level smoother, are known to be very ef ...

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MATHICSE Technical Report: Immersed Boundary-Conformal Isogeometric Method for Linear Elliptic Problems

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We present a novel isogeometric method, namely the Immersed Boundary-Conformal Method (IBCM), that features a layer of discretization conformal to the boundary while employing a simple background mesh for the remaining domain. In this manner, we leverage t ...

MATHICSE2021

Immersed boundary-conformal isogeometric method for linear elliptic problems

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2021

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