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A novel smooth immersed boundary method (IBM) based on a direct-forcing formulation is proposed to simulate incompressible dense particle-laden flows. This IBM relies on a regularization of the transfer function between the Eulerian grid…

Computational Physics · Physics 2023-04-24 Victor Chéron , Fabien Evrard , Berend van Wachem

The present contribution aims at developing a non-overlapping Domain Decomposition (DD) approach to the solution of acoustic wave propagation boundary value problems based on the Helmholtz equation, on both bounded and unbounded domains.…

Numerical Analysis · Mathematics 2026-01-26 Antonin Boisneault , Marcella Bonazzoli , Xavier Claeys , Pierre Marchand

We find solutions of Laplace's equation with specific boundary conditions (in which such solutions take either the value zero or unity in each surface) using a generic curvilinear system of coordinates. Such purely geometrical solutions…

Classical Physics · Physics 2015-04-01 Mayckol Morales , Rodolfo A. Diaz , William J. Herrera

Meshfree methods, including the reproducing kernel particle method (RKPM), have been widely used within the computational mechanics community to model physical phenomena in materials undergoing large deformations or extreme topology…

Numerical Analysis · Mathematics 2025-06-19 Jennifer E. Fromm , John A. Evans , J. S. Chen

We present a coupling of the Finite Element and the Boundary Element Method in an isogeometric framework to approximate either two-dimensional Laplace interface problems or boundary value problems consisting in two disjoint domains. We…

Numerical Analysis · Mathematics 2020-07-24 Mehdi Elasmi , Christoph Erath , Stefan Kurz

This paper presents a matrix-free approach for implementing the shifted boundary method (SBM) in finite element analysis. The SBM is a versatile technique for solving partial differential equations on complex geometries by shifting boundary…

Numerical Analysis · Mathematics 2025-07-24 Michał Wichrowski

The Generalized Method of Moments (GMM) is a partition of unity based technique for solving electromagnetic and acoustic boundary integral equations. Past work on the GMM for electromagnetics was confined to geometries modeled by piecewise…

Computational Physics · Physics 2015-06-18 Daniel Dault , Naveen V. Nair , Jie Li , Balasubramaniam Shanker

In this paper we apply the boundary elements method (BEM) and the dual reciprocity boundary elements method (DRBEM) for the numerical solution of two-dimensional time-fractional partial differential equations (TFPDEs). The fractional…

Numerical Analysis · Mathematics 2023-05-23 Peyman Alipour

The Reduced Basis Method (RBM) is a rigorous model reduction approach for solving parametrized partial differential equations. It identifies a low-dimensional subspace for approximation of the parametric solution manifold that is embedded…

Numerical Analysis · Mathematics 2018-09-25 Yanlai Chen , Jiahua Jiang , Akil Narayan

A novel boundary element method (BEM) removes the classical dependence on explicit fundamental solutions and extends quasi-optimal BEM discretisations to strongly elliptic operators with variable coefficients. The approach constructs a…

Numerical Analysis · Mathematics 2026-05-22 Benedikt Gräßle , Stefan A. Sauter

The method of fundamental solutions (MFS) is a numerical method for solving boundary value problems involving linear partial differential equations. It is well known that it can be very effective assuming regularity of the domain and…

Numerical Analysis · Mathematics 2022-03-23 Pedro R. S. Antunes

Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions. In this paper, a novel boundary integral formulation is proposed and its highly accurate…

Numerical Analysis · Mathematics 2020-07-20 Heping Dong , Jun Lai , Peijun Li

A radial basis function (RBF) method based on matrix-valued kernels is presented and analyzed for computing two types of vector decompositions on bounded domains: one where the normal component of the divergence-free part of the field is…

Numerical Analysis · Mathematics 2015-03-06 Edward J. Fuselier , Grady B. Wright

In this paper a characteristics-based open boundary condition (CBC) is proposed for the magnetohydrodynamic (MHD) system of equations. The algorithm is carefully designed and implemented in the context of a high-order flux reconstruction…

Computational Physics · Physics 2020-07-01 Xiaoliang Zhang , Chunlei Liang

We analyse a new subdomain scheme for a time-spectral method for solving initial boundary value problems. Whilst spectral methods are commonplace for spatially dependent systems, finite difference schemes are typically applied for the…

Computational Physics · Physics 2017-08-08 Kristoffer Lindvall , Jan Scheffel

A new projection method based on radial basis functions (RBFs) is presented for discretizing the incompressible unsteady Stokes equations in irregular geometries. The novelty of the method comes from the application of a new technique for…

Numerical Analysis · Mathematics 2015-09-21 Edward J. Fuselier , Varun Shankar , Grady B. Wright

A new technique is presented to solve a class of linear boundary value problems (BVP). Technique is primarily based on an operational matrix developed from a set of modified Bernoulli polynomials. The new set of polynomials is an…

Computational Engineering, Finance, and Science · Computer Science 2020-08-14 Udaya Pratap Singh

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…

Numerical Analysis · Mathematics 2021-08-04 Xiaodong Wei , Benjamin Marussig , Pablo Antolin , Annalisa Buffa

We present a novel integral-equation algorithm for evaluation of Zaremba eigenvalues and eigenfunctions}, that is, eigenvalues and eigenfunctions of the Laplace operator with mixed Dirichlet-Neumann boundary conditions; of course, (slight…

Numerical Analysis · Mathematics 2016-05-04 Eldar Akhmetgaliyev , Oscar Bruno , Nilima Nigam

In this work we develop a discretisation method for the Brinkman problem that is uniformly well-behaved in all regimes (as identified by a local dimensionless number with the meaning of a friction coefficient) and supports general meshes as…

Numerical Analysis · Mathematics 2023-03-22 Daniele A. Di Pietro , Jérôme Droniou