Related papers: Modeling irregular boundaries using isoparametric …
A novel multi-resolution technique called border mapping multi-resolution (BMMR) is proposed for projection-based particle methods. The BMMR aims to obtain background equivalent particle distributions in the two sides of a border between…
While the exterior Helmholtz problem with Dirichlet boundary conditions is always well-posed, the associated standard boundary integral equations are not if the squared wavenumber agrees with an eigenvalue of the interior Dirichlet problem.…
In the present thesis, a computational framework for the analysis of the deformation and damage phenomena occurring at the micro-scale of polycrystalline materials is presented. Micro-mechanics studies are commonly performed using the…
Metamaterials are artificially engineered structures that manipulate electromagnetic waves, having optical properties absent in natural materials. Recently, machine learning for the inverse design of metamaterials has drawn attention.…
The Monotonocity Principle (MP), stating a monotonic relationship between a material property and a proper corresponding boundary operator, is attracting great interest in the field of inverse problems, because of its fundamental role in…
We present a velocity-based moving mesh virtual element method for the numerical solution of PDEs involving moving boundaries. The virtual element method is used for computing both the mesh velocity and a conservative Arbitrary…
An inverse problem of identifying locations and certain properties of small dielectric inhomogeneities in a homogeneous background medium from boundary measurements on a part of the boundary is studied. Using as weights particular…
The paper outlines some recent developments of the boundary element method (BEM) that makes it more user friendly and suitable for a realistic simulation in geomechanics, especially for underground excavations and tunnelling. The…
In this work, we consider parabolic models with dynamic boundary conditions and parabolic bulk-surface problems in 3D. Such partial differential equations based models describe phenomena that happen both on the surface and in the…
This paper develops and investigates a new method for the application of Dirichlet boundary conditions for computational models defined by point clouds. Point cloud models often stem from laser or structured-light scanners which are used to…
We develop a new multiscale finite element method for Laplace equation with oscillating Neumann boundary conditions on rough boundaries. The key point is the introduction of a new boundary condition that incorporates both the…
We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…
The numerical performance of the material point method (MPM) is strongly governed by the particle-grid kernel, which controls the trade-off among smoothness, locality, numerical diffusion, contact accuracy, and computational cost. Although…
Dynamic shearing banding and fracturing in unsaturated porous media is a significant problem in engineering and science. This article proposes a multiphase micro-periporomechanics (uPPM) paradigm for modeling dynamic shear banding and…
A homogenization approach is one of effective strategies to solve multiscale elliptic problems approximately. The finite element heterogeneous multiscale method (FEHMM) which is based on the finite element makes possible to simulate such…
Capturing the interaction between objects that have an extreme difference in Young s modulus or geometrical scale is a highly challenging topic for numerical simulation. One of the fundamental questions is how to build an accurate…
We introduce a framework for the design of finite element methods for two-dimensional moving boundary problems with prescribed boundary evolution that have arbitrarily high order of accuracy, both in space and in time. At the core of our…
In this paper, we introduce a novel convex formulation that seamlessly integrates the Material Point Method (MPM) with articulated rigid body dynamics in frictional contact scenarios. We extend the linear corotational hyperelastic model…
Acoustic wave propagation through a homogeneous material embedded in an unbounded medium can be formulated as a boundary integral equation and accurately solved with the boundary element method. The computational efficiency deteriorates at…
Mixed boundary conditions are introduced to finite element exterior calculus. We construct smoothed projections from Sobolev de Rham complexes onto finite element de Rham complexes which commute with the exterior derivative, preserve…