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Topology optimization problems often support multiple local minima due to a lack of convexity. Typically, gradient-based techniques combined with continuation in model parameters are used to promote convergence to more optimal solutions;…

Numerical Analysis · Mathematics 2021-01-13 Ioannis P. A. Papadopoulos , Patrick E. Farrell , Thomas M. Surowiec

In this paper, the stabilized finite element approximation of the Stokes eigenvalue problems is considered for both the two-field (displacement-pressure) and the three-field (stress-displacement-pressure) formulations. The method presented…

Numerical Analysis · Mathematics 2016-09-21 Önder Türk , Daniele Boffi , Ramon Codina

We propose an upwind finite volume method for a system of two kinetic equations in one dimension that are coupled through nonlocal interaction terms. These cross-interaction systems were recently obtained as the mean-field limit of a…

Numerical Analysis · Mathematics 2023-09-15 Julia I. M. Hauser , Valeria Iorio , Markus Schmidtchen

We present a one-step algorithm that solves the Maxwell equations for systems with spatially varying permittivity and permeability by the Chebyshev method. We demonstrate that this algorithm may be orders of magnitude more efficient than…

Computational Physics · Physics 2009-11-07 H. De Raedt , K. Michielsen , J. S. Kole , M. T. Figge

Local time-stepping methods permit to overcome the severe stability constraint on explicit methods caused by local mesh refinement without sacrificing explicitness. In \cite{DiazGrote09}, a leapfrog based explicit local time-stepping…

Numerical Analysis · Mathematics 2022-04-05 Marcus J. Grote , Simon Michel , Stefan Sauter

Three algebraically stabilized finite element schemes for discretizing convection-diffusion-reaction equations are studied on adaptively refined grids. These schemes are the algebraic flux correction (AFC) scheme with Kuzmin limiter, the…

Numerical Analysis · Mathematics 2024-01-15 Abhinav Jha , Volker John , Petr Knobloch

We introduce a finite volume scheme for the two-dimensional incompressible Navier-Stokes equations. We use a triangular mesh. The unknowns for the velocity and pressure are both piecewise constant (colocated scheme). We use a projection…

Numerical Analysis · Mathematics 2007-05-23 Sebastien Zimmermann

We consider surface finite elements and a semi-implicit time stepping scheme to simulate fluid deformable surfaces. Such surfaces are modeled by incompressible surface Navier-Stokes equations with bending forces. Here, we consider closed…

Numerical Analysis · Mathematics 2023-05-03 Veit Krause , Axel Voigt

This note describes the full approximation storage (FAS) multigrid scheme for an easy one-dimensional nonlinear boundary value problem. The problem is discretized by a simple finite element (FE) scheme. We apply both FAS V-cycles and…

Numerical Analysis · Mathematics 2022-02-03 Ed Bueler

Parallel and cyclic projection algorithms are proposed for minimizing the sum of a finite family of convex functions over the intersection of a finite family of closed convex subsets of a Hilbert space. These algorithms are of…

Optimization and Control · Mathematics 2019-01-08 Hong-Kun Xu , Vera Roshchina

In this paper we present a Local Fourier Analysis of a space-time multigrid solver for a hyperbolic test problem. The space-time discretization is based on arbitrarily high order discontinuous Galerkin spectral element methods in time and a…

Numerical Analysis · Mathematics 2021-12-07 Lea M. Versbach , Philipp Birken , Viktor Linders , Gregor Gassner

We present and analyze a multiscale method for wave propagation problems, posed on spatial networks. By introducing a coarse scale, using a finite element space interpolated onto the network, we construct a discrete multiscale space using…

Numerical Analysis · Mathematics 2023-04-12 Morgan Görtz , Per Ljung , Axel Målqvist

The present paper addresses the convergence of a first order in time incremental projection scheme for the time-dependent incompressible Navier-Stokes equations to a weak solution, without any assumption of existence or regularity…

Numerical Analysis · Mathematics 2023-07-12 Thierry Gallouët , Raphaèle Herbin , Jean-Claude Latché , David Maltese

In this paper we are concerned with the stabilization of MUSCL-type finite volume schemes in arbitrary space dimensions. We consider a number of limited reconstruction techniques which are defined in terms inequality-constrained linear or…

Numerical Analysis · Mathematics 2017-01-24 Christoph Gersbacher , Martin Nolte

In this work, we propose a bi-grid scheme framework for the Allen-Cahn equation in Finite Element Method. The new methods are based on the use of two FEM spaces, a coarse one and a fine one, and on a decomposition of the solution into mean…

Numerical Analysis · Mathematics 2017-08-01 Hyam Abboud , Clara Al Kosseifi , Jean-Paul Chehab

We introduce a new formulation for the finite element immersed boundary method which makes use of a distributed Lagrange multiplier. We prove that a full discretization of our model, based on a semi-implicit time advancing scheme, is…

Numerical Analysis · Mathematics 2015-03-05 Daniele Boffi , Nicola Cavallini , Lucia Gastaldi

We investigate the long time behavior of solutions to a shape and topology optimization problem with respect to the time-dependent Navier--Stokes equations. The sought topology is represented by a stationary phase-field that represents a…

Optimization and Control · Mathematics 2026-05-04 Michael Hinze , Christian Kahle , John Sebastian H. Simon

This paper investigates an adaptive wavelet collocation time domain method for the numerical solution of Maxwell's equations. In this method a computational grid is dynamically adapted at each time step by using the wavelet decomposition of…

Numerical Analysis · Mathematics 2012-04-06 Haojun Li , Kirankumar R. Hiremath , Andreas Rieder , Wolfgang Freude

In this work, we propose and develop efficient and accurate numerical methods for solving the Kirchhoff-Love plate model in domains with complex geometries. The algorithms proposed here employ curvilinear finite-difference methods for…

Numerical Analysis · Mathematics 2021-05-13 Longfei Li , Hangjie Ji , Qi Tang

Finite element approximations of minimal surface are not always precise. They can even sometimes completely collapse. In this paper, we provide a simple and inexpensive method, in terms of computational cost, to improve finite element…

Numerical Analysis · Mathematics 2018-05-18 Aymeric Grodet , Takuya Tsuchiya