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Logarithmic conformation reformulations for viscoelastic constitutive laws have alleviated the high Weissenberg number problem, and the exploration of highly elastic flows became possible. However, stabilized formulations for logarithmic…

Computational Engineering, Finance, and Science · Computer Science 2021-12-14 Stefan Wittschieber , Leszek Demkowicz , Marek Behr

This work presents a new hybrid discretization approach to alleviate membrane locking in isogeometric finite element formulations for Kirchhoff-Love shells. The approach is simple, and requires no additional dofs and no static condensation.…

Computational Engineering, Finance, and Science · Computer Science 2025-09-09 Roger A. Sauer , Zhihui Zou , Thomas J. R. Hughes

Surface-subsurface flow models for hydrological applications solve a coupled multiphysics problem. This usually consists of some form of the Richards and shallow water equations. A typical setup couples these two nonlinear partial…

Numerical Analysis · Mathematics 2025-04-25 Valentina Schüller , Philipp Birken , Andreas Dedner

We introduce a new regularized interface method for proving existence of weak solutions to nonlinear moving boundary problems with low-regularity interfaces. We study a fluid-poroelastic structure interaction (FPSI) problem coupling the…

Analysis of PDEs · Mathematics 2025-08-26 Jeffrey Kuan , Sunčica Čanić , Boris Muha

Shells are ubiquitous thin structures that can undergo large nonlinear elastic deformations while exhibiting combined modes of bending and stretching, and have profound modern applications. In this paper, we have proposed a new Isogeometric…

Soft Condensed Matter · Physics 2022-06-22 Nikhil Padhye , Subodh Kalia

Easy to construct and optimally convergent generalisations of B-splines to unstructured meshes are essential for the application of isogeometric analysis to domains with non-trivial topologies. Nonetheless, especially for hexahedral meshes,…

Numerical Analysis · Mathematics 2022-07-27 Kim Jie Koh , Deepesh Toshniwal , Fehmi Cirak

This paper develops a unified theoretical framework for constructing B-spline basis function spaces with structural equivalence to finite element spaces. The theory rigorously establishes that these bases emerge as explicit linear…

Numerical Analysis · Mathematics 2026-01-29 Peng Yang , Maodong Pan , Falai Chen , Zhimin Zhang

Binary-fluid flows can be modeled using the Navier-Stokes-Cahn-Hilliard equations, which represent the boundary between the fluid constituents by a diffuse interface. The diffuse-interface model allows for complex geometries and topological…

An efficient computational approach for optimal reconstruction of binary-type images suitable for models in various applications including biomedical imaging is developed and validated. The methodology includes derivative-free optimization…

Optimization and Control · Mathematics 2022-09-27 Paul R. Arbic , Vladislav Bukshtynov

This work presents a numerical formulation to model isotropic viscoelastic material behavior for membranes and thin shells. The surface and the shell theory are formulated within a curvilinear coordinate system, which allows the…

Computational Engineering, Finance, and Science · Computer Science 2022-08-24 Karsten Paul , Roger A. Sauer

This paper presents a general theory and isogeometric finite element implementation for studying mass conserving phase transitions on deforming surfaces. The mathematical problem is governed by two coupled fourth-order nonlinear partial…

Compositional simulation is challenging, because of highly nonlinear couplings between multi-component flow in porous media with thermodynamic phase behavior. The coupled nonlinear system is commonly solved by the fully-implicit scheme.…

Computational Physics · Physics 2020-10-13 Jiamin Jiang , Xian-Huan Wen

The goal of this work is to improve focusing of high-intensity ultrasound by modifying the geometry of acoustic lenses through shape optimization. The shape optimization problem is formulated by introducing a tracking-type cost functional…

Optimization and Control · Mathematics 2017-12-15 Markus Muhr , Vanja Nikolić , Barbara Wohlmuth , Linus Wunderlich

This paper presents a new and unified approach to the derivation and analysis of many existing, as well as new discontinuous Galerkin methods for linear elasticity problems. The analysis is based on a unified discrete formulation for the…

Numerical Analysis · Mathematics 2021-10-12 Qingguo Hong , Jun Hu , Limin Ma , Jinchao Xu

In the context of isogeometric analysis, globally $C^1$ isogeometric spaces over unstructured quadrilateral meshes allow the direct solution of fourth order partial differential equations on complex geometries via their Galerkin…

Numerical Analysis · Mathematics 2018-12-24 Mario Kapl , Giancarlo Sangalli , Thomas Takacs

Complex geometries as common in industrial applications consist of multiple patches, if spline based parametrizations are used. The requirements for the generation of analysis-suitable models are increasing dramatically since isogeometric…

Computational Engineering, Finance, and Science · Computer Science 2020-10-30 Christian Hesch , Ustim Khristenko , Rolf Krause , Alexander Popp , Alexander Seitz , Wolfgang Wall , Barbara Wohlmuth

A novel approach which combines isogeometric collocation and an equilibrium-based stress recovery technique is applied to analyze laminated composite plates. Isogeometric collocation is an appealing strong form alternative to standard…

Numerical Analysis · Mathematics 2024-12-20 Alessia Patton , John-Eric Dufour , Pablo Antolin , Alessandro Reali

In this paper we develop an isogeometric B\'ezier dual mortar method for the biharmonic problem on multi-patch domains. The well-posedness of the discrete biharmonic problem requires a discretization with $C^1$ continuous basis functions.…

Numerical Analysis · Mathematics 2025-10-20 Di Miao , Michael A. Scott , Michael J. Borden , Derek C. Thomas , Zhihui Zou

This article focuses on the space-time isogeometric method for a linear time dependent fourth order problem. Using an auxiliary variable, first the problem is split into a system of two second order differential equations and then the…

Numerical Analysis · Mathematics 2025-01-13 Shreya Chauhan , Sudhakar Chaudhary

The construction of robust solvers for linear systems obtained from the discretization of partial differential equations using Isogeometric Analysis is challenging since the condition number of the system matrix not only grows with the…

Numerical Analysis · Mathematics 2025-12-24 Monica Montardini , Stefan Takacs , Mattia Tani