相关论文: RBF-based meshless boundary knot method and bounda…
We present a non-nested multilevel algorithm for solving the Poisson equation discretized at scattered points using polyharmonic radial basis function (PHS-RBF) interpolations. We append polynomials to the radial basis functions to achieve…
The immersed boundary (IB) method has been used as a means to simulate fluid-membrane interactions in a wide variety of biological and engineering applications. Although the numerical convergence of the method has been empirically verified,…
In this work, we propose a novel Bregman ADMM with nonlinear dual update to solve the Bethe variational problem (BVP), a key optimization formulation in graphical models and statistical physics. Our algorithm provides rigorous convergence…
We study the settling of solid particles within a viscous incompressible fluid contained in a two-dimensional channel, where the mass density of the particles is slightly greater than that of the fluid. The fluid-structure interaction…
The Wave Based Method (WBM) is a Trefftz method for the simulation of wave problems in vibroacoustics. Like other Trefftz methods, it employs a non-standard discretisation basis consisting of solutions of the partial differential equation…
This paper presents eigensolution and non-modal analyses for immersed boundary methods (IBMs) based on volume penalization for the linear advection equation. This approach is used to analyze the behavior of flux reconstruction (FR)…
The Immersed Boundary (IB) method of Peskin (J. Comput. Phys., 1977) is useful for problems involving fluid-structure interactions or complex geometries. By making use of a regular Cartesian grid that is independent of the geometry, the IB…
An isogeometric boundary element method for problems in elasticity is presented, which is based on an independent approximation for the geometry, traction and displacement field. This enables a flexible choice of refinement strategies,…
Consider the problem of minimizing the sum of a smooth convex function and a separable nonsmooth convex function subject to linear coupling constraints. Problems of this form arise in many contemporary applications including signal…
This work focuses on model preparation for electrostatic simulations of CAD designs to realize a rapid virtual prototyping concept. We present a boundary element method (BEM) allowing discontinuous fields between surfaces. The corresponding…
A discontinuous viscosity coefficient makes the jump conditions of the velocity and normal stress coupled together, which brings great challenges to some commonly used numerical methods to obtain accurate solutions. To overcome the…
We suggest a method for simultaneously generating high order quadrature weights for integrals over Lipschitz domains and their boundaries that requires neither meshing nor moment computation. The weights are determined on pre-defined…
We study the problem of minimizing the sum of three convex functions: a differentiable, twice-differentiable and a non-smooth term in a high dimensional setting. To this effect we propose and analyze a randomized block cubic Newton (RBCN)…
We present a boundary-spheropolygon element method (BSEM), that combines the boundary integral method (BIM) and the spheropolygon-based discrete element method (SEM). The interaction between particles is simulated via the SEM, and the…
A mesh-free approach for modelling beam-wall interactions in particle accelerators is proposed. The key idea of our method is to use a deep neural network as a surrogate for the solution to a set of partial differential equations involving…
We consider the EBT algorithm (a particle method) for the non-local equation with a discontinuous interaction kernel. The main difficulty lies in the low regularity of the kernel which is not Lipschitz continuous, thus preventing the…
High-order partial differential equations (PDEs) require derivative regularity that standard $C^0$ finite element infrastructures do not directly provide on unstructured meshes. We propose a mesh-intrinsic generalized finite element method…
Multidimensional population balance models (PBMs) describe chemical and biological processes having a distribution over two or more intrinsic properties (such as size and age, or two independent spatial variables). The incorporation of…
Consider the electromagnetic scattering of a time-harmonic plane wave by an open cavity which is embedded in a perfectly electrically conducting infinite ground plane. This paper is concerned with the numerical solutions of the transverse…
We present a new formulation of the Boundary Element Method (BEM) for simulating the non-adhesive and adhesive contact between an indenter of arbitrary shape and an elastic half-space coated with an elastic layer of different material. We…