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In this paper, we propose an efficient parallelization strategy for boundary element method (BEM) solvers that perform the electromagnetic analysis of structures with lossy conductors. The proposed solver is accelerated with the adaptive…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-11-30 Damian Marek , Shashwat Sharma , Piero Triverio

We consider the Weak Galerkin finite element approximation of the Singularly Perturbed Biharmonic elliptic problem on a unit square domain with clamped boundary conditions. Shishkin mesh is used for domain discretization as the solution…

Numerical Analysis · Mathematics 2024-09-12 Aayushman Raina , Srinivasan Natesan , Şuayip Toprakseven

The simulation of certain flow problems requires a means for modeling a free fluid surface; examples being viscoelastic die swell or fluid sloshing in tanks. In a finite-element context, this type of problem can, among many other options,…

Numerical Analysis · Mathematics 2017-09-21 Florian Zwicke , Sebastian Eusterholz , Stefanie Elgeti

This paper presents an iteration method for solving linear particle transport problems in binary stochastic mixtures. It is based on nonlinear projection approach. The method is defined by a hierarchy of equations consisting of the…

Numerical Analysis · Mathematics 2026-03-18 Dmitriy Y. Anistratov

Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their…

Numerical Analysis · Mathematics 2025-01-30 Nils Wunsch , Keenan Doble , Mathias R. Schmidt , Lise Noël , John A. Evans , Kurt Maute

This work develops a computational framework that combines physics-informed neural networks with multi-patch isogeometric analysis to solve partial differential equations on complex computer-aided design geometries. The method utilizes…

Computational Engineering, Finance, and Science · Computer Science 2025-10-01 Moritz von Tresckow , Ion Gabriel Ion , Dimitrios Loukrezis

This paper presents a shape optimisation system to design the shape of an acoustically-hard object in the three-dimensional open space. Boundary element method (BEM) is suitable to analyse such an exterior field. However, the conventional…

Numerical Analysis · Mathematics 2021-05-11 Toru Takahashi , Daisuke Sato , Hiroshi Isakari , Toshiro Matsumoto

The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially when the domain has a complex shape or adaptive refinement. We…

Numerical Analysis · Computer Science 2015-03-19 Peter R. Brune , Matthew G. Knepley , L. Ridgway Scott

We propose a boundary-corrected weak Galerkin mixed finite element method for solving elliptic interface problems in 2D domains with curved interfaces. The method is formulated on body-fitted polygonal meshes, where interface edges are…

Numerical Analysis · Mathematics 2025-02-06 Yongli Hou , Yi Liu , Yanqiu Wang

The concept of isogeometric analysis, whereby the parametric func- tions that are used to describe CAD geometry are also used to approx- imate the unknown fields in a numerical discretisation, has progressed rapidly in recent years. This…

Numerical Analysis · Mathematics 2013-02-22 R. N. Simpson , S. P. A. Bordas , H. Lian , J. Trevelyan

We introduce a discontinuous Galerkin method for the mixed formulation of the elasticity eigenproblem with reduced symmetry. The analysis of the resulting discrete eigenproblem does not fit in the standard spectral approximation framework…

Numerical Analysis · Mathematics 2018-01-29 Felipe Lepe , Salim Meddahi , David Mora , Rodolfo Rodríguez

We combine continuous and discontinuous Galerkin methods in the setting of a model diffusion problem. Starting from a hybrid discontinuous formulation, we replace element interiors by more general subsets of the computational domain -…

Computational Physics · Physics 2018-11-30 Martin Vymazal , David Moxey , Chris Cantwell , Spencer Sherwin , Robert M. Kirby

In this paper, we introduce a fast Fourier-Galerkin method for solving boundary integral equations on torus-shaped surfaces, which are diffeomorphic to a torus. We analyze the properties of the integral operator's kernel to derive the decay…

Numerical Analysis · Mathematics 2024-10-10 Yiying Fang , Ying Jiang , Jiafeng Su

Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…

Numerical Analysis · Mathematics 2024-02-27 Jennifer E. Fromm , Nils Wunsch , Kurt Maute , John A. Evans , Jiun-Shyan Chen

We present a strongly-coupled immersed-boundary method for flow-structure interaction problems involving thin deforming bodies. The method is stable for arbitrary choices of solid-to-fluid mass ratios and for large body motions. As with…

Fluid Dynamics · Physics 2016-10-05 Andres Goza , Tim Colonius

Although Galerkin discretizations have been intensively employed in the IgA context, an efficient implementation requires special numerical quadrature rules when constructing the system of equations. To avoid this issue, isogeometric…

Numerical Analysis · Mathematics 2017-11-30 Fabio Roman

The matrix formation associated to high-order discretizations is known to be numerically demanding. Based on the existing procedure of interpolation and lookup, we design a multiscale assembly procedure to reduce the exorbitant assembly…

Numerical Analysis · Mathematics 2021-07-21 Thibaut Hirschler , Pablo Antolin , Annalisa Buffa

This paper is concerned with the Boundary Element simulation of elastic domains that contain thin inclusions that have elastic material properties, which are different to the domain. With thin inclusions we mean inclusions with extreme…

Numerical Analysis · Mathematics 2025-05-27 Vincenzo Mallardo , Christian Dunser , Gernot Beer

We formulate and analyze an adaptive algorithm for isogeometric analysis with hierarchical B-splines for weakly-singular boundary integral equations. We prove that the employed weighted-residual error estimator is reliable and converges at…

Numerical Analysis · Mathematics 2022-08-24 Gregor Gantner , Dirk Praetorius

The proximal Galerkin finite element method is a high-order, low-iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of point-wise bound constraints in infinite-dimensional function spaces.…

Numerical Analysis · Mathematics 2024-12-18 Brendan Keith , Thomas M. Surowiec