Related papers: A Finite Element Based P3M Method for N-body Probl…
This article's main scope is the presentation of a computational method for the simulation of contact problems within the finite element method involving complex and rough surfaces. The approach relies on the MPJR (eMbedded Profile for…
Chaotic free surface flows are challenging problems to simulate numerically, mainly due to the significant changes in geometry and frequent topological changes. Methods that track the evolution of the fluid in a Lagrangian formulation are a…
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…
In this paper we present a Fourier feature based deep domain decomposition method (F-D3M) for partial differential equations (PDEs). Currently, deep neural network based methods are actively developed for solving PDEs, but their efficiency…
Cut finite element method (CutFEM) based approaches towards challenging fluid-structure interaction (FSI) are proposed. The different considered methods combine the advantages of competing novel Eulerian (fixed-grid) and established…
A novel Material Point Method (MPM) is introduced for addressing frictional contact problems. In contrast to the standard multi-velocity field approach, this method employs a penalty method to evaluate contact forces at the discretised…
The Fast Multipole Method (FMM) offers an acceleration for pairwise interaction calculation, known as $N$-body problems, from $\mathcal{O}(N^2)$ to $\mathcal{O}(N)$ with $N$ particles. This has brought dramatic increase in the capability of…
We consider a mesh-based approach for training a neural network to produce field predictions of solutions to parametric partial differential equations (PDEs). This approach contrasts current approaches for "neural PDE solvers" that employ…
The paper studies a method for solving elliptic partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method allows a surface to be given implicitly as a zero level of a level set function. A surface equation…
We consider discrete Poisson interface problems resulting from linear unfitted finite elements, also called cut finite elements (CutFEM). Three of these unfitted finite element methods known from the literature are studied. All three…
We present a new composite mesh finite element method for fluid--structure interaction problems. The method is based on surrounding the structure by a boundary-fitted fluid mesh which is embedded into a fixed background fluid mesh. The…
Effective field theories (EFTs) are widely used to study many-body systems by describing two-body interactions using zero-ranged contact potentials. However, when extended to three-body processes, these contact interactions lead to…
This paper presents a unified and computationally efficient framework for predicting incompressible, irrotational (potential) flow around multiple immersed bodies in two-dimensional domains, with particular emphasis on quantifying…
This paper introduces BFEMP, a new approach for monolithically coupling the Material Point Method (MPM) with the Finite Element Method (FEM) through barrier energy-based particle-mesh frictional contact using a variational time-stepping…
The Tree-Particle-Mesh (TPM) N-body algorithm couples the tree algorithm for directly computing forces on particles in an hierarchical grouping scheme with the extremely efficient mesh based PM structured approach. The combined TPM…
This work presents the Griffith-type phase-field formation at large deformation in the framework of adaptive edge-based smoothed finite element method (ES-FEM) for the first time. Therein the phase-field modeling of fractures has attracted…
We demonstrate that scalable neuromorphic hardware can implement the finite element method, which is a critical numerical method for engineering and scientific discovery. Our approach maps the sparse interactions between neighboring finite…
The objective of this work is the development of a novel finite element formulation describing the contact interaction of slender beams in complex 3D configurations involving arbitrary beam-to-beam orientations. It is shown in a…
We present a new fixed mesh algorithm for solving a class of interface inverse problems for the typical elliptic interface problems. These interface inverse problems are formulated as shape optimization prob- lems whose objective…
A simple and efficient interface-fitted mesh generation algorithm is developed in this paper. This algorithm can produce a local anisotropic fitting mixed mesh which consists of both triangles and quadrilaterals near the interface. A new…