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This paper presents a decomposition method for solving elliptic boundary value problems in one-dimension. The method is an improvement to an existing technique for approximating elliptic systems. It is demonstrated to be computationally…

Analysis of PDEs · Mathematics 2024-10-10 Christian O. Bernal Zelaya , Prosper Torsu

Elliptic interface problems whose solutions are $C^0$ continuous have been well studied over the past two decades. The well-known numerical methods include the strongly stable generalized finite element method (SGFEM) and immersed FEM…

Numerical Analysis · Mathematics 2023-02-28 Champike Attanayake , So-Hsiang Chou , Quanling Deng

In this paper, we present a new numerical method for determining the numerical solution of interface problems to optimal accuracy with respect to the polynomial order of the Lagrangian finite element space on polytopial meshes. We introduce…

Numerical Analysis · Mathematics 2018-03-13 Pavel Bochev , James Cheung , Max Gunzburger , Mauro Perego

Elliptic partial differential equations arise in many fields of science and engineering such as steady state distribution of heat, fluid dynamics, structural/mechanical engineering, aerospace engineering and seismology etc. In three…

Numerical Analysis · Mathematics 2011-10-12 Akhlaq Husain

In this paper we apply the INTERNODES method to solve second order elliptic problems discretized by Isogeometric Analysis methods on non-conforming multiple patches in 2D and 3D geometries. INTERNODES is an interpolation-based method that,…

Numerical Analysis · Mathematics 2019-10-10 Paola Gervasio , Federico Marini

Achieving strongly symmetric stress approximations for linear elasticity problems in high-contrast media poses a significant computational challenge. Conventional methods often struggle with prohibitively high computational costs due to…

Numerical Analysis · Mathematics 2025-09-03 Eric T. Chung , Changqing Ye , Xiang Zhong

For interface tracking of an arbitrary number of materials in two dimensions, we propose a multiphase cubic MARS method that (a) represents the topology and geometry of the interface via graphs, cycles, and cubic splines, (b) applies to any…

Numerical Analysis · Mathematics 2026-04-06 Yan Tan , Yixiao Qian , Zhiqi Li , Qinghai Zhang

We introduce a new class of mixed finite element methods for 2D and 3D compressible nonlinear elasticity. The independent unknowns of these conformal methods are displacement, displacement gradient, and the first Piola-Kirchhoff stress…

Numerical Analysis · Mathematics 2019-10-22 Arzhang Angoshtari , Ali Gerami Matin

For most finite element simulations, boundary-conforming meshes have significant advantages in terms of accuracy or efficiency. This is particularly true for complex domains. However, with increased complexity of the domain, generating a…

Numerical Analysis · Mathematics 2021-04-07 Jan Helmig , Fabian Key , Marek Behr , Stefanie Elgeti

We study the problem of designing systems in order to minimize cost while meeting a given flexibility target. Flexibility is attained by enforcing a joint chance constraint, which ensures that the system will exhibit feasible operation with…

Optimization and Control · Mathematics 2021-06-25 Joshua L. Pulsipher , Victor M. Zavala

In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. We consider a new unfitted finite element method…

Numerical Analysis · Mathematics 2017-06-27 Christoph Lehrenfeld , Arnold Reusken

This work outlines a new multi-physics-compatible immersed rigid body method for Eulerian finite-volume simulations. To achieve this, rigid bodies are represented as a diffuse scalar field and an interface seeding method is employed to…

Computational Physics · Physics 2022-03-15 Tim Wallis , Philip Barton , Nikolaos Nikiforakis

Elastic similarity measures are fundamental to time series similarity search because of their ability to handle temporal misalignments. These measures are inherently computationally expensive, therefore necessitating the use of lower bounds…

Databases · Computer Science 2026-03-20 Zemin Chao , Boyu Xiao , Zitong Li , Zhixin Qi , Xianglong Liu , Hongzhi Wang

We consider a model for the evolution of an interface in a heterogeneous environment governed by a parabolic equation. The heterogeneity is introduced as obstacles exerting a localized dry friction. Our main result establishes the emergence…

Analysis of PDEs · Mathematics 2019-09-12 Luca Courte , Patrick Dondl , Ulisse Stefanelli

In this study, we investigate and compare formulations for computing shape derivatives in bi-material level-set optimization with precise modeling of the interface. The level-set function is parameterized using B-splines, whose coordinates…

Classical Physics · Physics 2024-10-30 Majd Kosta , Oded Amir

We present a barrier method for treating frictional contact on interfaces embedded in finite elements. The barrier treatment has several attractive features, including: (i) it does not introduce any additional degrees of freedom or…

Numerical Analysis · Mathematics 2022-06-17 Yidong Zhao , Jinhyun Choo , Yupeng Jiang , Minchen Li , Chenfanfu Jiang , Kenichi Soga

The design of contact interfaces that meet quantitatively a specified friction law (friction force vs normal force) is challenging due to the multi-scale and multi-physics nature of contact interactions. Recently, a concept was proposed to…

The design space of dynamic multibody systems (MBSs), particularly those with flexible components, is considerably large. Consequently, having a means to efficiently explore this space and find the optimum solution within a feasible…

Optimization and Control · Mathematics 2025-01-08 Mehran Ebrahimi , Adrian Butscher , Hyunmin Cheong , Francesco Iorio

We present, to the best of our knowledge, the first complete three-dimensional numerical solutions to a broad range of boundary value problems for a general theory of finite strain gradient elasticity. We have chosen for our work, Toupin's…

Mathematical Physics · Physics 2015-08-24 Shiva Rudraraju , Anton van der Ven , Krishna Garikipati

In this paper, we study the stability and convergence of a decoupled and linearized mixed finite element method (FEM) for incompressible miscible displacement in a porous media whose permeability and porosity are discontinuous across some…

Numerical Analysis · Mathematics 2014-06-18 Buyang Li , Hongxing Rui , Chaoxia Yang