Related papers: From geometric design to numerical analysis: A dir…
This study develops a polygonal cell-based smoothed finite element method (CSFEM) for two-dimensional seepage analyses in porous media, covering steady-state, transient, and free-surface problems. Wachspress interpolation on convex…
In this paper, we analyze the embedding cell method, an algorithm which has been developed for the numerical homogenization of metal-ceramic composite materials. We show the convergence of the iteration scheme of this algorithm and the…
Trimming is a core technique in geometric modeling. Unfortunately, the resulting objects do not take the requirements of numerical simulations into account and yield various problems. This paper outlines principal issues of trimmed models…
The difficulties in dealing with discontinuities related to a sharp crack are overcome in the phase-field approach for fracture by modeling the crack as a diffusive object being described by a continuous field having high gradients. The…
This work presents a practical finite element modeling strategy, the Crack Element Method (CEM), for simulating the dynamic crack propagation in two-dimensional structures. The method employs an element-splitting algorithm based on the…
The concept of isogeometric analysis, whereby the parametric func- tions that are used to describe CAD geometry are also used to approx- imate the unknown fields in a numerical discretisation, has progressed rapidly in recent years. This…
Mesoscale simulations of woven composites using parameterized analytical geometries offer a way to connect constituent material properties and their geometric arrangement to effective composite properties and performance. However, the…
Isogeometric analysis (IGA) is a numerical method that connects computer-aided design (CAD) with finite element analysis (FEA). In CAD the computational domain is usually represented by B-spline or NURBS patches. Given a NURBS…
The fixed point construction is a method for designing tile sets and cellular automata with highly nontrivial dynamical and computational properties. It produces an infinite hierarchy of systems where each layer simulates the next one. The…
Implicit neural representations have emerged as a powerful approach for encoding complex geometries as continuous functions. These implicit models are widely used in computer vision and 3D content creation, but their integration into…
Using an interface inserted in a background mesh is an alternative way of constructing a complex geometrical shape with a relative low meshing efforts. However, this process may require special treatment of elements cut by the interface.…
Implicitly described domains are a well established tool in the simulation of time dependent problems, e.g. using level-set methods. In order to solve partial differential equations on such domains, a range of numerical methods was…
An accurate, physically-based, and differentiable model of soft robots can unlock downstream applications in optimal control. The Finite Element Method (FEM) is an expressive approach for modeling highly deformable structures such as…
Cell blebs are protrusions of the cell membrane and can be instrumental for cell migration. We derive a continuum model for the mechanical and geometrical aspects of the onset of blebbing in terms of a force balance. It is abstract and…
Isogeometrically enriched finite elements offer efficient localized isogeometric analysis (IGA) enrichment for numerical simulations involving large computational domains. This is achieved by employing surface enriched elements to interface…
We focus on the finite element method computations with higher-order C1 continuity basis functions that preserve the partition of unity. We show that the rows of the system of linear equations can be combined, and the test functions can be…
The Finite Element Method (FEM) is a powerful modeling tool for predicting the behavior of soft robots. However, its use for control can be difficult for non-specialists of numerical computation: it requires an optimization of the…
The lattice Boltzmann method has become a widely adopted approach in computational fluid dynamics, offering unique advantages in mesoscopic kinetic modeling, intrinsic parallelism, and simple treatment of boundary conditions. However, its…
Using exact computer arithmetic, it is possible to determine the (exact) solution of a numerical model without rounding error. For such purposes, a corresponding system of equations should be exactly defined, either directly or by…
The traditional workflow in continuum mechanics simulations is that a geometry description -- for example obtained using Constructive Solid Geometry or Computer Aided Design tools -- forms the input for a mesh generator. The mesh is then…