Related papers: A nested Schur complement solver with mesh-indepen…
In this paper we deal with diffusive relaxation limits of nonlinear systems of Euler type modeling chemotactic movement of cells toward Keller--Segel type systems. The approximating systems are either hyperbolic--parabolic or…
Two-place nonlocal systems have attracted many scientists' attentions. In this paper, two-place non-localities are extended to multi-place non-localities. Especially, various two-place and four-place nonlocal nonlinear Schrodinger (NLS)…
Recently, integrability conditions (ICs) in mutistate Landau-Zener (MLZ) theory were proposed [1]. They describe common properties of all known solved systems with linearly time-dependent Hamiltonians. Here we show that ICs enable efficient…
An inherent regularization strategy and block Schur complement preconditioning are studied for linear poroelasticity problems discretized using the lowest-order weak Galerkin FEM in space and the implicit Euler scheme in time. At each time…
For an isotropic and homogeneous nonlinear left-handed materials, for which the effective medium approximation is valid, Maxwell's equations for electric and magnetic fields lead naturally, within the slowly varying envelope approximation,…
The formal Heisenberg equations of the Federbush model are linearized and then are directly integrated applying the method of dynamical mappings. The fundamental role of two-dimensional free massless pseudo-scalar fields is revealed for…
A two component nonlocal vector nonlinear Schr\"odinger equation (VNLSE) is considered with a self-induced $ {\cal PT}$ symmetric potential. It is shown that the system possess a Lax pair and an infinite number of conserved quantities and…
On a smooth, closed Riemannian manifold, we study the question of proportionality of components, also called synchronization, of vector-valued solutions to nonlinear elliptic Schr\"odinger systems with constant coefficients. In particular,…
We investigate the dynamical behavior of continuous and discrete Schrodinger systems exhibiting parity-time (PT) invariant nonlinearities. We show that such equations behave in a fundamentally different fashion than their nonlinear…
An integrable two-component nonlinear Schr\"odinger equation in $2+1$ dimensions is presented. The singular manifold method is applied in order to obtain a three-component Lax pair. The Lie point symmetries of this Lax pair are calculated…
This paper addresses the construction and analysis of a class of domain decomposition methods for the iterative solution of the quasi-static Biot problem in three-field formulation. The considered discrete model arises from time…
We present a scalable, parallel implementation of a solver for the solution of a phase-field model for quasi-static brittle fracture. The code is available as open source. Numerical solutions in 2d and 3d with adaptive mesh refinement show…
Based on the Suzuki product-formula approach, we construct a family of unconditionally stable algorithms to solve the time-dependent Maxwell equations. We describe a practical implementation of these algorithms for one-, two-, and…
We propose an approach to obtaining explicit estimates on the resolvent of hypocoercive operators by using Schur complements, rather than from an exponential decay of the evolution semigroup combined with a time integral. We present…
We propose a new concept of strong controllability associated with the Schur complement of a suitable limiting matrix. This concept allows us to extend the previous results associated with multidimensional ARX models. On the one hand, we…
This paper introduces an extension of the time-splitting sine-spectral (TSSP) method for solving damped focusing nonlinear Schr\"{o}dinger equations (NLS). The method is explicit, unconditionally stable and time transversal invariant.…
This paper aims to investigate the numerical approximation of semilinear non-autonomous stochastic partial differential equations (SPDEs) driven by multiplicative or additive noise. Such equations are more realistic than autonomous SPDEs…
We introduce Power Bundle Adjustment as an expansion type algorithm for solving large-scale bundle adjustment problems. It is based on the power series expansion of the inverse Schur complement and constitutes a new family of solvers that…
For time integration of transient eddy current problems commonly implicit time integration methods are used, where in every time step one or several nonlinear systems of equations have to be linearized with the Newton-Raphson method due to…
We study finite element approximations of elliptic and parabolic interface problems with discontinuous coefficients and nonlinear jump conditions. We introduce a scalar interface reduction in which the solution is decomposed into a…