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We present benchmark computations of dynamic poroelasticity modeling fluid flow in deformable porous media by a coupled hyperbolic-parabolic system of partial differential equations. A challenging benchmark setting and goal quantities of…

Numerical Analysis · Mathematics 2023-07-06 Mathias Anselmann , Markus Bause , Nils Margenberg , Pavel Shamko

We explore quantitative descriptors that herald when a many-particle system in $d$-dimensional Euclidean space $\mathbb{R}^d$ approaches a hyperuniform state as a function of the relevant control parameter. We establish quantitative…

Soft Condensed Matter · Physics 2021-05-26 Salvatore Torquato

We study mixed finite element methods for the rotating shallow water equations with linearized momentum terms but nonlinear drag. By means of an equivalent second-order formulation, we prove long-time stability of the system without energy…

Numerical Analysis · Mathematics 2017-06-06 Colin J. Cotter , P. Jameson Graber , Robert C. Kirby

A cornerstone of numerical homogenization is the equivalence of the microscopic and the macroscopic energy densities, which is referred to as Hill-Mandel condition. Among these coupling conditions, the cases of periodic, linear displacement…

Numerical Analysis · Mathematics 2019-06-26 Andreas Fischer , Bernhard Eidel

Heating generated by high-intensity focused ultrasound waves is central to many emerging medical applications, including non-invasive cancer therapy and targeted drug delivery. In this study, we aim to gain a fundamental understanding of…

Numerical Analysis · Mathematics 2025-10-03 Julio Careaga , Benjamin Dörich , Vanja Nikolić

We study optimal design problems where the design corresponds to a coefficient in the principal part of the state equation. The state equation, in addition, is parameter dependent, and we allow it to change type in the limit of this…

Optimization and Control · Mathematics 2024-12-09 Tadele Mengesha , Abner J. Salgado , Joshua M. Siktar

In recent years, an increasing attention has been paid to quantum heterostructures with tailored functionalities, such as heterojunctions and quantum matematerials, in which quantum dynamics of electrons can be described by the…

Numerical Analysis · Mathematics 2024-12-20 Jingrun Chen , Dingjiong Ma , Zhiwen Zhang

Under compressive creep, visco-plastic solids experiencing internal mass transfer processes have been recently proposed to accommodate singular cnoidal wave solutions, as material instabilities at the stationary wave limit. These…

Computational Physics · Physics 2020-08-05 Roberto J. Cier , Thomas Poulet , Sergio Rojas , Victor M. Calo , Manolis Veveakis

We consider a parameter dependent family of damped hyperbolic equations with interesting limit behavior: the system approaches steady states exponentially fast and for parameter to zero the solutions converge to that of a parabolic limit…

Numerical Analysis · Mathematics 2017-04-19 Herbert Egger , Thomas Kugler

We present a model of the hydraulic fracturing of heterogeneous poroelastic media. The formalism is an effective continuum model that captures the coupled dynamics of the fluid pressure and the fractured rock matrix and models both the…

Materials Science · Physics 2015-06-05 Kjetil M. D. Hals , Inga Berre

A nonlocal model of peridynamic type for dynamic brittle damage is introduced consisting of two phases, one elastic and the other inelastic. Evolution from the elastic to the inelastic phase depends on material strength. Existence and…

Analysis of PDEs · Mathematics 2024-04-02 Robert P. Lipton , Debdeep Bhattacharya

The subject of this article is a matched microstructure model for Newtonian fluid flows in fractured porous media. This is a homogenized model which takes the form of two coupled parabolic differential equations with boundary conditions in…

Analysis of PDEs · Mathematics 2011-12-21 Joachim Escher , Daniela Treutler

Due to their algorithmic simplicity and high accuracy, force-based model coupling techniques are an exciting development in computational physics. For example, the force-based quasicontinuum approximation is the only known pointwise…

Numerical Analysis · Mathematics 2015-05-13 Matthew Dobson , Mitchell Luskin , Christoph Ortner

A state-based peridynamic formulation for linear elastic shells is presented. The emphasis is on introducing, possibly for the first time, a general surface based peridynamic model to represent the deformation characteristics of structures…

Computational Physics · Physics 2015-08-04 Shubhankar Roy Chowdhury , Pranesh Roy , Debasish Roy , J. N. Reddy

A recently introduced particle-based model for fluid dynamics with continuous velocities is generalized to model fluids with excluded volume effects. This is achieved through the use of biased stochastic multi-particle collisions which…

Soft Condensed Matter · Physics 2007-05-23 Erkan Tuzel , Thomas Ihle , Daniel M. Kroll

We consider a finite element approximation for a system consisting of the evolution of a curve evolving by forced curve shortening flow coupled to a reaction-diffusion equation on the evolving curve. The curve evolves inside a given domain…

Numerical Analysis · Mathematics 2020-04-22 Vanessa Styles , James Van Yperen

In this contribution we present how to obtain explicit state space models in port-Hamiltonian form when a mixed finite element method is applied to a linear mechanical system with non-uniform boundary conditions. The key is to express the…

Systems and Control · Electrical Eng. & Systems 2021-11-01 Tobias Thoma , Paul Kotyczka

In this paper, we propose a linear and monolithic finite element method for the approximation of an incompressible viscous fluid interacting with an elastic and deforming plate. We use the arbitrary Lagrangian-Eulerian (ALE) approach that…

Numerical Analysis · Mathematics 2023-01-13 Sebastian Schwarzacher , Bangwei She , Karel Tuma

This paper studies the numerical analysis of a parameter identification problem governed by elliptic equations with power-type nonlinearity. We propose a numerical reconstruction via a suitable least-squares minimization problem based on…

Numerical Analysis · Mathematics 2026-03-10 De-Han Chen , Yi-Hsuan Lin , Irwin Yousept

We consider the evolution of curve networks in two dimensions (2d) and surface clusters in three dimensions (3d). The motion of the interfaces is described by surface diffusion, with boundary conditions at the triple junction points/lines,…

Numerical Analysis · Mathematics 2022-11-07 Weizhu Bao , Harald Garcke , Robert Nürnberg , Quan Zhao