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pro vyhledávání: '"Papadopoulos , Ioannis"'
We develop a semismooth Newton framework for the numerical solution of fixed-point equations that are posed in Banach spaces. The framework is motivated by applications in the field of obstacle-type quasi-variational inequalities and implicit obstacl
Externí odkaz:
http://arxiv.org/abs/2409.19637
We develop a sparse hierarchical $hp$-finite element method ($hp$-FEM) for the Helmholtz equation with rotationally invariant variable coefficients posed on a two-dimensional disk or annulus. The mesh is an inner disk cell (omitted if on an annulus d
Externí odkaz:
http://arxiv.org/abs/2402.12831
We show, in one dimension, that an $hp$-Finite Element Method ($hp$-FEM) discretisation can be solved in optimal complexity because the discretisation has a special sparsity structure that ensures that the \emph{reverse Cholesky factorisation} -- Cho
Externí odkaz:
http://arxiv.org/abs/2402.11299
Exceptionally elegant formulae exist for the fractional Laplacian operator applied to weighted classical orthogonal polynomials. We utilize these results to construct a solver, based on frame properties, for equations involving the fractional Laplaci
Externí odkaz:
http://arxiv.org/abs/2311.12451
We prove and collect numerous explicit and computable results for the fractional Laplacian $(-\Delta)^s f(x)$ with $s>0$ as well as its whole space inverse, the Riesz potential, $(-\Delta)^{-s}f(x)$ with $s\in\left(0,\frac{1}{2}\right)$. Choices of $
Externí odkaz:
http://arxiv.org/abs/2311.10896
We discuss computing with hierarchies of families of (potentially weighted) semiclassical Jacobi polynomials which arise in the construction of multivariate orthogonal polynomials. In particular, we outline how to build connection and differentiation
Externí odkaz:
http://arxiv.org/abs/2310.07541
Autor:
Papadopoulos, Ioannis P. A.
We study the finite element approximation of the solid isotropic material with penalization (SIMP) model for the topology optimization problem of minimizing the compliance of a linearly elastic structure. To ensure the existence of a local minimizer
Externí odkaz:
http://arxiv.org/abs/2211.04249