The unstable nature of the material point method (MPM) is widely documented and is a
barrier to the method being used for routine engineering analyses of large deformation …

A high-order accurate implicit-mesh discontinuous Galerkin framework for wave propagation
in single-phase and bi-phase solids is presented. The framework belongs to the embedded …

The complex geometries of real-world problems pose a considerable challenge to the
preprocessing of the standard finite element method (FEM), wherein the mesh conforms to …

Radial basis function generated finite difference (RBF-FD) methods for PDEs require a set of
interpolation points which conform to the computational domain Ω. One of the requirements …

We present new stabilization terms for solving the linear transport equation on a cut cell
mesh using the discontinuous Galerkin (DG) method in two dimensions with piecewise …

In this work, we present the Domain of Dependence (DoD) stabilization for systems of
hyperbolic conservation laws in one space dimension. The base scheme uses a method of …

A high-order cut finite element method is formulated for solving the elastic wave equation.
Both a single domain problem and an interface problem are treated. The boundary or …

In this paper, we develop a family of high order cut discontinuous Galerkin (DG) methods for
hyperbolic conservation laws in one space dimension. Ghost penalty stabilization is used to …

In this paper we develop a fully explicit cut finite element method for the wave equation. The
method is based on using a standard leap frog scheme combined with an extension …

We propose a method to solve the acoustic wave equation on an immersed domain using
the hybridizable discontinuous Galerkin method for spatial discretization and the arbitrary …