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We present a parallel-scalable method for simulating non-dilute suspensions of deformable particles immersed in Stokesian fluid in three dimensions. A critical component in these simulations is robust and accurate collision handling. This…

Numerical Analysis · Mathematics 2018-12-13 Libin Lu , Abtin Rahimian , Denis Zorin

We consider a Navier-Stokes fluid-plate interaction (FSI) system which describes the evolutions of the fluid contained within a 3D cavity, as it interacts with a deformable elastic membrane on the ``free" upper boundary of the cavity. These…

Analysis of PDEs · Mathematics 2025-07-04 Pelin G. Geredeli , Quyuan Lin , Dylan Mcknight , Mohammad Mahabubur Rahman

Computational fluid dynamics (CFD) studies have been increasingly used for blood flow simulations in intracranial aneurysms (ICAs). However, despite the continuous progress of body-fitted CFD solvers, generating a high quality mesh is still…

Computational Engineering, Finance, and Science · Computer Science 2020-07-28 D. S. Lampropoulos , G. C. Bourantas , B. F. Zwick , G. C. Kagadis , A. Wittek , K. Miller , V. C. Loukopoulos

Understanding the behavior of biomolecules such as proteins requires understanding the critical influence of the surrounding fluid (solvent) environment--water with mobile salt ions such as sodium. Unfortunately, for many studies, fully…

Soft Condensed Matter · Physics 2015-05-27 J. P. Bardhan , D. A. Tejani , N. S. Wieckowski , A. Ramaswamy , M. G. Knepley

We present a spectrally-accurate scheme to turn a boundary integral formulation for an elliptic PDE on a single unit cell geometry into one for the fully periodic problem. Applications include computing the effective permeability of…

Numerical Analysis · Mathematics 2016-11-28 Alex H. Barnett , Gary Marple , Shravan Veerapaneni , Lin Zhao

The Immersed Boundary (IB) method of Peskin (J. Comput. Phys., 1977) is useful for problems involving fluid-structure interactions or complex geometries. By making use of a regular grid that is independent of the geometry, the IB framework…

Numerical Analysis · Mathematics 2022-10-17 Brittany J. Leathers

We present an efficient B-spline finite element method (FEM) for cloth simulation. While higher-order FEM has long promised higher accuracy, its adoption in cloth simulators has been limited by its larger computational costs while…

Graphics · Computer Science 2026-05-05 Yuqi Meng , Yihao Shi , Kemeng Huang , Zixuan Lu , Ning Guo , Taku Komura , Yin Yang , Minchen Li

In the study of micro-swimmers, both artificial and biological ones, many-query problems arise naturally. Even with the use of advanced high performance computing (HPC), it is not possible to solve this kind of problems in an acceptable…

Numerical Analysis · Mathematics 2020-08-04 Nicola Giuliani , Martin W. Hess , Antonio DeSimone , Gianluigi Rozza

In this work we present a novel bulk-surface virtual element method (BSVEM) for the numerical approximation of elliptic bulk-surface partial differential equations (BSPDEs) in three space dimensions. The BSVEM is based on the discretisation…

Numerical Analysis · Mathematics 2023-05-24 Massimo Frittelli , Anotida Madzvamuse , Ivonne Sgura

In this paper, we define new unfitted finite element methods for numerically approximating the solution of surface partial differential equations using bulk finite elements. The key idea is that the $n$-dimensional hypersurface, $\Gamma…

Numerical Analysis · Mathematics 2014-03-21 Klaus Deckelnick , Charles M. Elliott , Thomas Ranner

In this paper, we develop two parameter-robust numerical algorithms for Biot model and applied the algorithms in brain edema simulations. By introducing an intermediate variable, we derive a multiphysics reformulation of the Biot model.…

Numerical Analysis · Mathematics 2019-06-24 Guoliang Jv , Mingchao Cai , Jingzhi Li , Jing Tian

This paper introduces the scaled boundary cubature (SBC) scheme for accurate and efficient integration of functions over polygons and two-dimensional regions bounded by parametric curves. Over two-dimensional domains, the SBC method reduces…

Numerical Analysis · Mathematics 2021-11-09 Eric B. Chin , N. Sukumar

Electrostatic forces play many important roles in molecular biology, but are hard to model due to the complicated interactions between biomolecules and the surrounding solvent, a fluid composed of water and dissolved ions. Continuum model…

Numerical Analysis · Mathematics 2015-12-29 Jaydeep P. Bardhan , Matthew G. Knepley

We present a simple modification of the direct-forcing immersed boundary method (IBM) proposed by Uhlmann [J. Comput. Phys, 2005] in order to enable it to be applied to particulate flows with solid-to-fluid density ratios around unity. The…

Fluid Dynamics · Physics 2023-06-21 Manuel Garcia-Villalba , Blanca Fuentes , Jan Dusek , Manuel Moriche , Markus Uhlmann

We provide exact solutions of the Stokes equations for a squirming sphere close to a no-slip surface, both planar and spherical, and for the interactions between two squirmers, in three dimensions. These allow the hydrodynamic interactions…

Fluid Dynamics · Physics 2017-04-05 Dario Papavassiliou , Gareth P. Alexander

Despite rapid progress in the development of quantum algorithms in quantum computing as well as numerical simulation methods in classical computing for atomic and molecular applications, no systematic and comprehensive electronic structure…

A data-driven surrogate framework to accelerate particle-resolved modelling of quasi-dilute suspensions of rigid, non-spherical particles in Stokes flow is introduced. A regularized-Stokeslet boundary element method (BEM) is implemented to…

Fluid Dynamics · Physics 2025-12-17 Marco Laudato

We introduce a new "convolution spline" temporal approximation of time domain boundary integral equations (TDBIEs). It shares some properties of convolution quadrature (CQ), but instead of being based on an underlying ODE solver the…

Numerical Analysis · Mathematics 2014-05-08 Penny J Davies , Dugald B Duncan

This paper introduces a sharp interface method to simulate fluid-structure interaction (FSI) involving rigid bodies immersed in viscous incompressible fluids. The capabilities of this methodology are demonstrated for a range of benchmark…

The method of fundamental solutions (MFS) is known to be effective for solving 3D Laplace and Stokes Dirichlet boundary value problems in the exterior of a large collection of simple smooth objects. Here we present new scalable MFS…

Numerical Analysis · Mathematics 2025-08-22 Anna Broms , Alex H. Barnett , Anna-Karin Tornberg