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The quad-curl problem arises in the study of the electromagnetic interior transmission problem and magnetohydrodynamics (MHD). In this paper, we study the quad-curl eigenvalue problem and propose a mixed method using edge elements for the…

Numerical Analysis · Mathematics 2013-10-25 Jiguang Sun

We present a simple and effective multigrid-based Poisson solver of second-order accuracy in both gravitational potential and forces in terms of the one, two and infinity norms. The method is especially suitable for numerical simulations…

Computational Physics · Physics 2020-03-04 Hsiang-Hsu Wang , Chien-Chang Yen

We present a multigrid iterative algorithm for solving a system of coupled free boundary problems for pricing American put options with regime-switching. The algorithm is based on our recently developed compact finite difference scheme…

Computational Finance · Quantitative Finance 2021-11-09 Chinonso Nwankwo , Weizhong Dai

In this work, we present a combination of a multigrid approach and the phi-FEM immersed boundary finite element method to reduce its computational cost while preserving its accuracy. To further reduce the numerical cost of the approach, we…

Numerical Analysis · Mathematics 2026-05-14 Raphaël Bulle , Michel Duprez , Vanessa Lleras , Killian Vuillemot

An efficient nonlinear multigrid method for a mixed finite element method of the Darcy-Forchheimer model is constructed in this paper. A Peaceman-Rachford type iteration is used as a smoother to decouple the nonlinearity from the divergence…

Numerical Analysis · Mathematics 2017-04-27 Jian Huang , Long Chen , Hongxing Rui

When used to accelerate the convergence of fixed-point iterative methods, such as the Picard method, which is a kind of nonlinear fixed-point iteration, polynomial extrapolation techniques can be very effective. The numerical solution of…

Numerical Analysis · Mathematics 2025-01-07 Abdellatif Mouhssine , Ahmed Ratnani , Hassane Sadok

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

In this paper, we present a nonnested augmented subspace algorithm and its multilevel correction method for solving eigenvalue problems with curved interfaces. The augmented subspace algorithm and the corresponding multilevel correction…

Numerical Analysis · Mathematics 2020-11-17 Haikun Dang , Hehu Xie , Gang Zhao , Chenguang Zhou

We propose some multigrid methods for solving the algebraic systems resulting from finite element approximations of space fractional partial differential equations (SFPDEs). It is shown that our multigrid methods are optimal, which means…

Numerical Analysis · Mathematics 2018-07-27 Yingjun Jiang , Xuejun Xu

A self-learning algebraic multigrid method for dominant and minimal singular triplets and eigenpairs is described. The method consists of two multilevel phases. In the first, multiplicative phase (setup phase), tentative singular triplets…

Numerical Analysis · Mathematics 2011-02-07 Hans De Sterck

Fourth-order differential equations play an important role in many applications in science and engineering. In this paper, we present a three-field mixed finite-element formulation for fourth-order problems, with a focus on the effective…

Numerical Analysis · Mathematics 2022-10-13 Patrick E. Farrell , Abdalaziz Hamdan , Scott P. MacLachlan

A simple and efficient interface-fitted mesh generation algorithm is developed in this paper. This algorithm can produce a local anisotropic fitting mixed mesh which consists of both triangles and quadrilaterals near the interface. A new…

Numerical Analysis · Mathematics 2020-05-13 Jun Hu , Hua Wang

In this paper we prove the optimal convergence of a standard adaptive scheme based on edge finite elements for the approximation of the solutions of the eigenvalue problem associated with Maxwell's equations. The proof uses the known…

Numerical Analysis · Mathematics 2018-04-09 Daniele Boffi , Lucia Gastaldi

The main of this work is to use the unit lower triangular matrices for solving inverse eigenvalue problem of nonnegative matrices and present the easier method to solve this problem.

Numerical Analysis · Mathematics 2018-05-22 Alimohammad Nazari , Atiyeh Nezami

We apply the method of inverse iteration to the Laplace eigenvalue problem with Robin and mixed Dirichlet-Neumann boundary conditions, respectively. For each problem, we prove convergence of the iterates to a non-trivial principal…

Analysis of PDEs · Mathematics 2025-06-03 Benjamin Lyons , Emily Ruttenberg , Nicholas Zitzelberger

In this paper, we present a multi-level mixed element scheme for the Helmholtz transmission eigenvalue problem on polygonal domains that are not necessarily able to be covered by rectangle grids. We first construct an equivalent linear…

Numerical Analysis · Mathematics 2017-07-04 Y. Xi , X. Ji , S. Zhang

Recently, a new eigenvalue problem, called the transmission eigenvalue problem, has attracted many researchers. The problem arose in inverse scattering theory for inhomogeneous media and has important applications in a variety of inverse…

Numerical Analysis · Mathematics 2016-11-23 Ruihao Huang , Allan A. Struthers , Jiguang Sun , Ruming Zhang

In this paper, using the linearization technique we write the Helmholtz transmission eigenvalue problem as an equivalent nonselfadjoint linear eigenvalue problem whose left-hand side term is a selfadjoint, continuous and coercive…

Numerical Analysis · Mathematics 2016-03-03 Yidu Yang , Jiayu Han , Hai Bi

It is known that the solution of a conservative steady-state two-sided fractional diffusion problem can exhibit singularities near the boundaries. As consequence of this, and due to the conservative nature of the problem, we adopt a finite…

Numerical Analysis · Mathematics 2022-09-20 Marco Donatelli , Rolf Krause , Mariarosa Mazza , Ken Trotti

In this paper, we perform a comparison study of two methods (the embedded boundary method and several versions of the mixed finite element method) to solve an elliptic boundary value problem.

Numerical Analysis · Mathematics 2013-04-23 Jian Du , Shuqiang Wang , James Glimm , Roman Samulyak