Related papers: Spectral boundary conditions for volumetric frame …
Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations. In particular, a knowledge of the symmetries may help reduce the problem dimension, cut…
Frames have established themselves as a means to derive redundant, yet stable decompositions of a signal for analysis or transmission, while also promoting sparse expansions. However, when the signal dimension is large, the computation of…
The aim of this study is to analyze the properties of harmonic fields in the vicinity of rough boundaries where either a constant potential or a zero flux is imposed, while a constant field is prescribed at an infinite distance from this…
Automating the solutions of multiple network information theory problems, stretching from fundamental concerns such as determining all information inequalities and the limitations of linear codes, to applied ones such as designing coded…
Rapid developments in the emerging field of stretchable and conformable photonics necessitate analytical expressions for boundary conditions at metasurfaces of arbitrary geometries. Here, we introduce the concept of conformal boundary…
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…
A numerical scheme to compute the spectrum of a large class of self-adjoint extensions of the Laplace-Beltrami operator on manifolds with boundary in any dimension is presented. The algorithm is based on the characterisation of a large…
The classical level set method, which represents the boundary of the unknown geometry as the zero-level set of a function, has been shown to be very effective in solving shape optimization problems. The present work addresses the issue of…
Determining the number of embeddings of Laman graph frameworks is an open problem which corresponds to understanding the solutions of the resulting systems of equations. In this paper we investigate the bounds which can be obtained from the…
Quadratic surfaces gain more and more attention among the Geometric Algebra community and some frameworks were proposed in order to represent, transform, and intersect these quadratic surfaces. As far as the authors know, none of these…
Fourth-order differential equations play an important role in many applications in science and engineering. In this paper, we present a three-field mixed finite-element formulation for fourth-order problems, with a focus on the effective…
Surfaces are typically represented as meshes, which can be extracted from volumetric fields via meshing or optimized directly as surface parameterizations. Volumetric representations occupy 3D space and have a large effective receptive…
We present a 3D hybrid method which combines the Finite Element Method (FEM) and the Spectral Boundary Integral method (SBIM) to model nonlinear problems in unbounded domains. The flexibility of FEM is used to model the complex,…
In a plethora of applications dealing with inverse problems, e.g. in image processing, social networks, compressive sensing, biological data processing etc., the signal of interest is known to be structured in several ways at the same time.…
We consider minimization problems with structured objective function and smooth constraints, and present a flexible framework that combines the beneficial regularization effects of (exact) penalty and interior-point methods. In the fully…
We present a fully analytic approach for evaluating boundary integrals in two dimensions for Smoothed Particle Hydrodynamics (SPH). Conventional methods often rely on boundary particles or wall re-normalization approaches derived from…
In this paper, we introduce a new method for applying the implicit function theorem to find nontrivial solutions to overdetermined problems with a fixed boundary (given) and a free boundary (to be determined). The novelty of this method…
We prove the global in time existence of spherically symmetric solutions to an initial-boundary value problem for a system of partial differential equations, which consists of the equations of linear elasticity and a nonlinear,…
We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…
Complicated boundary conditions are essential to accurately describe phenomena arising in nature and engineering. Recently, the investigation of a potential speedup through quantum algorithms in simulating the governing ordinary and partial…