相关论文: Second-kind integral equations for the Laplace-Bel…
The Laplace-Beltrami problem on closed surfaces embedded in three dimensions arises in many areas of physics, including molecular dynamics (surface diffusion), electromagnetics (harmonic vector fields), and fluid dynamics (vesicle…
The Laplace-Beltrami problem on closed surfaces embedded in three dimensions arises in many areas of physics, including molecular dynamics (surface diffusion), electromagnetics (harmonic vector fields), and fluid dynamics (vesicle…
This work presents uniform preconditioners for the discrete Laplace--Beltrami operator on hypersurfaces. In particular, within the framework of fast auxiliary space preconditioning (FASP), we develop efficient and user-friendly multilevel…
The Laplace-Beltrami operator on (the surface of) a triaxial ellipsoid admits a sequence of real eigenvalues diverging to plus infinity. By introducing ellipsoidal coordinates, this eigenvalue problem for a partial differential operator is…
Integral equation methods for solving the Laplace-Beltrami equation on the unit sphere in the presence of multiple "islands" are presented. The surface of the sphere is first mapped to a multiply-connected region in the complex plane via a…
We approximate the solution of the equation $$ -\Delta_S u+u = f $$ on a two-dimensional, embedded, orientable, closed surface $S$ where $-\Delta_S$ denotes the Laplace Beltrami operator on $S$ by using continuous, piecewise linear finite…
The inversion of the Laplace-Beltrami operator and the computation of the Hodge decomposition of a tangential vector field on smooth surfaces arise as computational tasks in many areas of science, from computer graphics to machine learning…
Many boundary element integral equation kernels are based on the Green's functions of the Laplace and Helmholtz equations in three dimensions. These include, for example, the Laplace, Helmholtz, elasticity, Stokes, and Maxwell's equations.…
Partial differential equations posed on surfaces arise in a number of applications. In this survey we describe three popular finite element methods for approximating solutions to the Laplace-Beltrami problem posed on an $n$-dimensional…
We study Laplace-type operators on hybrid manifolds, i.e. on configurations consisting of closed two-dimensional manifolds and one-dimensional segments. Such an operator can be constructed by using the Laplace-Beltrami operators on each…
The convergence problem of the Laplace-Beltrami operators plays an essential role in the convergence analysis of the numerical simulations of some important geometric partial differential equations which involve the operator. In this note…
We consider solving the Laplace-Beltrami problem on a smooth two dimensional surface embedded into a three dimensional space meshed with tetrahedra. The mesh does not respect the surface and thus the surface cuts through the elements. We…
Elliptic problems along smooth surfaces embedded in three dimensions occur in thin-membrane mechanics, electromagnetics (harmonic vector fields), and computational geometry. In this work, we present a parametrix-based integral equation…
A practical solution for the mathematical problem of functional calculus with Laplace-Beltrami operator on surfaces with axial symmetry is found. A quantitative analysis of the spectrum is presented.
We consider numerical approximations of spectral fractional Laplace-Beltrami problems on closed surfaces. The proposed numerical algorithms rely on their Balakrishnan integral representation and consist of a sinc quadrature coupled with…
An isogeometric approach for solving the Laplace-Beltrami equation on a two-dimensional manifold embedded in three-dimensional space using a Galerkin method based on Catmull-Clark subdivision surfaces is presented and assessed. The…
We propose an extension of the plane-wave representation for wave fields defined on the real sphere $\mathcal{S}^2$. This representation is well-known in the planar setting but has never been developed for curved surfaces. To achieve this,…
We present a simple yet accurate method to compute the adjoint double layer potential, which is used to solve the Neumann boundary value problem for Laplace's equation in three dimensions. An expansion in curvilinear coordinates leads us to…
Numerical solutions of partial differential equations (PDEs) on manifolds continues to generate a lot of interest among scientists in the natural and applied sciences. On the other hand, recent developments of 3D scanning and computer…
We prove new a posteriori error estimates for surface finite element methods (SFEM). Surface FEM approximate solutions to PDE posed on surfaces. Prototypical examples are elliptic PDE involving the Laplace-Beltrami operator. Typically the…