Landesman–Lazer type conditions and quasilinear elliptic equations
Strong resonance problems for the one-dimensional -Laplacian.
Přechodem hory k řešení okrajové úlohy
Drobná překvapení spojená s numerickou integrací
Effective semi-analytic integration for hypersingular Galerkin boundary integral equations for the Helmholtz equation in 3D
We deal with the Galerkin discretization of the boundary integral equations corresponding to problems with the Helmholtz equation in 3D. Our main result is the semi-analytic integration for the bilinear form induced by the hypersingular operator. Such computations have already been proposed for the bilinear forms induced by the single-layer and the double-layer potential operators in the monograph The Fast Solution of Boundary Integral Equations by O. Steinbach and S. Rjasanow and we base our computations...
Kouzlo Fibonacciho kódování
2-dimensional primal domain decomposition theory in detail
We give details of the theory of primal domain decomposition (DD) methods for a 2-dimensional second order elliptic equation with homogeneous Dirichlet boundary conditions and jumping coefficients. The problem is discretized by the finite element method. The computational domain is decomposed into triangular subdomains that align with the coefficients jumps. We prove that the condition number of the vertex-based DD preconditioner is , independently of the coefficient jumps, where and denote...
On conditioning of Schur complements of H-TFETI clusters for 2D problems governed by Laplacian
Bounds on the spectrum of the Schur complements of subdomain stiffness matrices with respect to the interior variables are key ingredients in the analysis of many domain decomposition methods. Here we are interested in the analysis of floating clusters, i.e. subdomains without prescribed Dirichlet conditions that are decomposed into still smaller subdomains glued on primal level in some nodes and/or by some averages. We give the estimates of the regular condition number of the Schur complements...
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