Related papers: Streamline integration as a method for two-dimensi…
A fusion boundary-plasma domain is defined by axisymmetric magnetic surfaces where the geometry is often complicated by the presence of one or more X-points; and modeling boundary plasmas usually relies on computational grids that account…
New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate first order derivative at the interface (from each side).…
We consider geometric multigrid methods for the solution of linear systems arising from isogeometric discretizations of elliptic partial differential equations. For classical finite elements, such methods are well known to be fast solvers…
The arrangement of network nodes in hyperbolic spaces has become a widely studied problem, motivated by numerous results suggesting the existence of hidden metric spaces behind the structure of complex networks. Although several methods…
The speed of sound in two-phase pipe flow systems is often several orders of magnitude greater than the travelling speed of hydraulic information (volume fractions.) Dynamically simulating such flows requires resolution of acoustic and…
In this paper, we describe a robust algorithm for 2-Manifold generation of various kinds of ShapeNet Models. The input of our pipeline is a triangle mesh, with a set of vertices and triangular faces. The output of our pipeline is a…
In this paper we present a one dimensional second order accurate method to solve Elliptic equations with discontinuous coefficients on an arbitrary interface. Second order accuracy for the first derivative is obtained as well. The method is…
The multigrid algorithm is a multilevel approach to accelerate the numerical solution of discretized differential equations in physical problems involving long-range interactions. Multiresolution analysis of wavelet theory provides an…
This paper presents a novel spline-based meshing technique that allows for usage of boundary-conforming meshes for unsteady flow and temperature simulations in co-rotating twin-screw extruders. Spline-based descriptions of arbitrary screw…
In this work, we develop algebraic solvers for linear systems arising from the discretization of second-order elliptic partial differential equations by saddle-point mixed finite element methods of arbitrary polynomial degree $p \ge 0$ on…
Elliptic partial differential equations are important both from application and analysis points of views. In this paper we apply the Closest Point Method to solving elliptic equations on general curved surfaces. Based on the closest point…
Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…
Multiscale methods for second order elliptic equations based on non-overlapping domain decomposition schemes have great potential to take advantage of multi-core, state-of-the-art parallel computers. These methods typically involve solving…
Orthogonal graph drawing has many applications, e.g., for laying out UML diagrams or cableplans. In this paper, we present a new pipeline that draws multigraphs orthogonally, using few bends, few crossings, and small area. Our pipeline…
We consider discontinuous Galerkin methods for an elliptic distributed optimal control problem and we propose multigrid methods to solve the discretized system. We prove that the $W$-cycle algorithm is uniformly convergent in the energy…
An expandable local and parallel two-grid finite element scheme based on superposition principle for elliptic problems is proposed and analyzed in this paper by taking example of Poisson equation. Compared with the usual local and parallel…
For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…
We present a technique novel in numerical methods. It compiles the domain of the numerical methods as a discretized volume. Congruent elements are glued together to compile the domain over which the solution of a boundary value problem of a…
Gridshells are defined as structures that have the shape and rigidity of a double curvature shell but consist of a grid instead of a continuous surface. This study concerns those obtained by elastic deformation of an initially flat two-way…
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…