Related papers: Efficient boundary corrected Strang splitting
This work presents the design of nonlinear stabilization techniques for the finite element discretization of Euler equations in both steady and transient form. Implicit time integration is used in the case of the transient form. A…
A rigorous convergence analysis of the Strang splitting algorithm with a discontinuous Galerkin approximation in space for the Vlasov--Poisson equations is provided. It is shown that under suitable assumptions the error is of order…
Modeling the chemical, electric, and thermal transport as well as phase transitions and the accompanying mesoscale microstructure evolution within a material in an electronic device setting involves the solution of partial differential…
Dynamic optimisation occurs in a variety of real-world problems. To tackle these problems, evolutionary algorithms have been extensively used due to their effectiveness and minimum design effort. However, for dynamic problems, extra…
The method of constructing approximate solutions of the first boundary value problem for linear differential equations based on incomplete (even and odd) trigonometric splines is considered. The theoretical positions are illustrated by…
The state transition algorithm (STA), as an intelligent optimization method grounded in constructivist learning, has been demonstrated to be highly effective in solving complex optimization problems. However, the standard STA suffers from…
Several strategies for nonlinearity mitigation based on signal processing at the transmitter and/or receiver side are analyzed and their effectiveness is discussed. Improved capacity lower bounds based on their combination are presented.
We continue the program initiated in a previous work, of applying integro-differential methods to Neumann Homogenization problems. We target the case of linear periodic equations with a singular drift, which includes (with some regularity…
The theory of matrix splitting is a useful tool for finding solution of rectangular linear system of equations, iteratively. The purpose of this paper is two-fold. Firstly, we revisit theory of weak regular splittings for rectangular…
For the numerical solution of Dirichlet-type boundary value problems associated to nonlinear fractional differential equations of order $\alpha \in (1,2)$ that use Caputo derivatives, we suggest to employ shooting methods. In particular, we…
We consider a class of second-order Strang splitting methods for Allen-Cahn equations with polynomial or logarithmic nonlinearities. For the polynomial case both the linear and the nonlinear propagators are computed explicitly. We show that…
Suitable discretizations through tensor product formulas of popular multidimensional operators (diffusion or diffusion--advection, for instance) lead to matrices with $d$-dimensional Kronecker sum structure. For evolutionary Partial…
In this paper we apply a scaling invariance analysis to reduce a class of parabolic moving boundary problems to free boundary problems governed by ordinary differential equations. As well known free boundary problems are always non-linear…
A hybrid framework combining the branch and bound method with multiobjective evolutionary algorithms is proposed for nonconvex multiobjective optimization. The hybridization exploits the complementary character of the two optimization…
We approximate the solution for the time dependent Schr\"odinger equation (TDSE) in two steps. We first use a pseudo-spectral collocation method that uses samples of functions on rank-1 or rank-r lattice points with unitary Fourier…
Statistical preconditioning enables fast methods for distributed large-scale empirical risk minimization problems. In this approach, multiple worker nodes compute gradients in parallel, which are then used by the central node to update the…
We propose a variant of the classical conditional gradient method for sparse inverse problems with differentiable measurement models. Such models arise in many practical problems including superresolution, time-series modeling, and matrix…
High-order finite difference methods are efficient, easy to program, scales well in multiple dimensions and can be modified locally for various reasons (such as shock treatment for example). The main drawback have been the complicated and…
We present an accelerated, or 'look-ahead' version of the Newton-Dinkelbach method, a well-known technique for solving fractional and parametric optimization problems. This acceleration halves the Bregman divergence between the current…
A Dirichlet-type problem is studied for an equation of even order with variable coefficients. A criterion for the uniqueness of a solution is given. The solution is built in the form of a Fourier series. When justifying the convergence of…