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The detailed implementation and analysis of a finite element multigrid scheme for the solution of elliptic optimal control problems is presented. A particular focus is in the definition of smoothing strategies for the case of constrained control problems. For this setting, convergence of the multigrid scheme is discussed based on the BPX framework. Results of numerical experiments are reported to...
Sparse grids, combined with gradient penalties provide an attractive tool for regularised least squares fitting. It has earlier been found that the combination technique, which builds a sparse grid function using a linear combination of approximations on partial grids, is here not as effective as it is in the case of elliptic partial differential equations. We argue that this is due to the irregular...
The present article deals with fictitious domain methods for numerical realization of scalar variational inequalities with the Signorini type conditions on the boundary. Two variants are introduced and analyzed. A discretization is done by finite elements. It leads to a system of non-smooth, piecewise linear equations. This system is solved by the semismooth Newton method. Numerical experiments confirm...
In this paper, we give an analysis and a general procedure for 4D variational data assimilation (4D-Var). In functional partial differential equation setting, the adjoint equation method, sensitivity analysis, and multicomponent operator splitting are discussed. Nonlinear optimization methods and convergence analysis are also investigated for 4D-Var.
In the paper we deal with lower bounds constructed for the asymptotic competitive ratio of semi-online bin packing and batched bin packing algorithms.We determine the bounds as the solutions of a related nonlinear optimization problem using theoretical analysis and a reliable numerical global optimization method. Our results improve the lower bounds given in Gutin et al. (Discrete Optim 2:71–82, 2005)...
Realistic mathematical models of physical processes contain uncertainties. These models are often described by stochastic differential equations (SDEs) or stochastic partial differential equations (SPDEs) with multiplicative noise. The uncertainties in the right-hand side or the coefficients are represented as random fields. To solve a given SPDE numerically one has to discretise the deterministic...
A matching $${E_\mathcal{M}}$$ of graph G = (V, E) is a subset of the edges E, such that no vertex in V is incident to more than one edge in $${E_\mathcal{M}}$$ . The matching $${E_\mathcal{M}}$$ is maximum if there is no matching in G with size strictly larger than the size of $${E_\mathcal{M}}$$ . In this paper, we present a distributed stabilizing algorithm for finding maximum...
We present a new algorithm, based on integral equation formulations, for the solution of constant-coefficient elliptic partial differential equations (PDE) in closed two-dimensional domains with non-smooth boundaries; we focus on cases in which the integral-equation solutions as well as physically meaningful quantities (such as, stresses, electric/magnetic fields, etc.) tend to infinity at singular...
In this paper, the maximal abelian dimension is computationally obtained for an arbitrary finite-dimensional Lie algebra, defined by its nonzero brackets. More concretely, we describe and implement an algorithm which computes such a dimension by running it in the symbolic computation package MAPLE. Finally, we also show a computational study related to this implementation, regarding both the computing...
In this paper, we propose a numerical scheme which is almost second-order spatial accurate for a one-dimensional singularly perturbed parabolic convection-diffusion problem exhibiting a regular boundary layer. The proposed numerical scheme consists of classical backward-Euler method for the time discretization and a hybrid finite difference scheme for the spatial discretization. We analyze the scheme...
In this paper, spectral properties and computational performance of a generalized block triangular preconditioner for symmetric saddle point problems are discussed in detail. We will provide estimates for the region containing both the nonreal and the real eigenvalues and generalize the results of Simoncini (Appl Numer Math 49:63–80, 2004) and Cao (Appl Numer Math 57:899–910, 2007). Finally, numerical...
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