相关论文: Intrinsic Integration
Boundary integral equation methods are widely used in the solution of many partial differential equations. The kernels that appear in these surface integrals are nearly singular when evaluated near the boundary, and straightforward…
We introduce a numerical method for reconstructing a multidimensional surface using the gradient of the surface measured at some values of the coordinates. The method consists of defining a multidimensional spline function and minimizing…
Several problems in magnetically confined fusion, such as the computation of exterior vacuum fields or the decomposition of the total magnetic field into separate contributions from the plasma and the external sources, are best formulated…
We suggest a finite element method for computing minimal surfaces based on computing a discrete Laplace-Beltrami operator operating on the coordinates of the surface. The surface is a discrete representation of the zero level set of a…
Unfitted (also known as embedded or immersed) finite element approximations of partial differential equations are very attractive because they have much lower geometrical requirements than standard body-fitted formulations. These schemes do…
This paper presents a regularization technique for the high order efficient numerical evaluation of nearly singular, principal-value, and finite-part Cauchy-type integral operators. By relying on the Cauchy formula, the Cauchy-Goursat…
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…
Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…
The Intrinsic Surface Finite Element Method (ISFEM) was recently proposed to solve Partial Differential Equations (PDEs) on surfaces. ISFEM proceeds by writing the PDE with respect to a local coordinate system anchored to the surface and…
In this paper we present a new Eulerian finite element method for the discretization of scalar partial differential equations on evolving surfaces. In this method we use the restriction of standard space-time finite element spaces on a…
We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets…
Surface integral equations (SIEs)-based boundary element methods are widely used for analyzing electromagnetic scattering scenarii. However, after discretization of SIEs, the spectrum and eigenvectors of the boundary element matrices are…
We introduce a new class of unfitted finite element methods with high order accurate numerical integration over curved surfaces and volumes which are only implicitly defined by level set functions. An unfitted finite element method which is…
Harmonic decomposition of surfaces, such as spherical and spheroidal harmonics, is used to analyze morphology, reconstruct, and generate surface inclusions of particulate microstructures. However, obtaining high-quality meshes of…
Scale analysis based on coarse-graining has been proposed recently as an alternative to Fourier analysis. It is now broadly used to analyze energy spectra and energy transfers in eddy-resolving ocean simulations. However, for data from…
We present a geometric multilevel optimization approach that smoothly incorporates box constraints. Given a box constrained optimization problem, we consider a hierarchy of models with varying discretization levels. Finer models are…
This paper presents a high-order accurate numerical quadrature algorithm for evaluating integrals over curved surfaces and regions defined implicitly via a level set of a given function restricted to a hyperrectangle. The domain is divided…
Many surface reconstruction methods incorporate normal integration, which is a process to obtain a depth map from surface gradients. In this process, the input may represent a surface with discontinuities, e.g., due to self-occlusion. To…
In this paper we propose a method for estimating depth from a single image using a coarse to fine approach. We argue that modeling the fine depth details is easier after a coarse depth map has been computed. We express a global (coarse)…
Singular and oscillatory functions feature in numerous applications. The high-accuracy approximation of such functions shall greatly help us develop high-order methods for solving applied mathematics problems. This paper demonstrates that…