Volume-fitted meshes have been widely used in different kinds of hydrodynamic models as well as in many hydro-mechanical models. A new method based on geographic information systems (GIS) has been presented to generate such irregular meshes automatically, which is also derived from classical algebraic methods on generating such meshes in hydrodynamics. Main inputs of the algorithm are DEM grids...

1. Abstract This paper introduces h-Adaptive eXtended Finite Element Method (X-FEM) which is used for level set based structural optimization. Compared to X-FEM with uniform meshes, meshes of h-adaptive X-FEM are adequately adjusted so that meshes of higher resolution at the vicinity of the structural boundaries while meshes of relatively lower resolution in the regions far away from boundaries...

In many coupled problems of practical interest the domain of at least one of the problems evolves in time. The Arbitrary Eulerian Lagrangian (ALE) approach is a tool very often employed to cope with this domain motion. However, in this work we aim at describing numerical techniques that allow us to use a fixed mesh for the approximation of moving boundary problems, particularly using the finite...

In this paper, a class of third order singularly perturbed boundary value problems with suitable boundary conditions is considered. The third order boundary value problem is transformed to asymptotically equivalent second order boundary value problem. This problem is solved efficiently by using fitted Numerov method. Linear and non-linear examples are solved to illustrate the method and relativ...

ICEM AutoHexa is a high-speed, object-based, fully-automated, high-quality, body-fitted hexahedral mesher that can be used to create unstructured hexahedral meshes. The input to ICEM AutoHexa is a set of axis aligned blocks, rectangles, cylinders, discs, and triangular prisms. Associated to each object are meshing parameters that control the density of the mesh. Because the geometric coverage i...

During simulations of complex engineering processes that include the domain evolution in time and space, it is often impossible to predict which regions should have finer numerical discretization advance. In such cases, adaptive mesh refinement (AMR) can be used achieve higher accuracy solution for as little computational cost possible. This achieved by locally refining only areas interest, lea...

We present a Conforming Delaunay Triangulation (CDT) algorithm based on maximal Poisson disk sampling. Points are unbiased, meaning the probability of introducing a vertex in a disk-free subregion is proportional to its area, except in a neighborhood of the domain boundary. In contrast, Delaunay refinement CDT algorithms place points dependent on the geometry of empty circles in intermediate tr...

In this paper we develop a new limiter for linear reconstruction on non-coordinatealigned meshes in two space dimensions, with focus on Cartesian embedded boundary grids. Our limiter is inherently two-dimensional and linearity preserving. It separately limits the x and y components of the gradient, as opposed to a scalar limiter which limits all components simultaneously with one scalar. The li...

We propose a new strategy for boundary conforming meshing that decouples the problem of building tetrahedra of proper size and shape from the problem of conforming to complex, non-manifold boundaries. This approach is motivated by the observation that while several methods exist for adaptive tetrahedral meshing, they typically have difficulty at geometric boundaries. The proposed strategy avoid...

We consider the hp–version interior penalty discontinuous Galerkin finite element method (hp–DGFEM) for semilinear parabolic equations with mixed Dirichlet and Neumann boundary conditions. Our main concern is the error analysis of the hp–DGFEM on shape–regular spatial meshes. We derive error bounds under various hypotheses on the regularity of the solution, for both the symmetric and non–symmet...