arXiv subjects

Rosa Donat

Publications and source records attributed to Rosa Donat.

4 recordsLinked to original sources

arXiv2022

A Multiresolution approach to solve large-scale optimization problems

General purpose optimization techniques can be used to solve many problems in engineering computations, although their cost is often prohibitive when the number of degrees of freedom is very large. We describe a multilevel approach to speed up the computation of the solution of a large-scale optimization problem by a given optimization technique. By embedding the problem within Harten's Multiresolution Framework (MRF), we set up a procedure that leads to the desired solution, after the computation of a finite sequence of sub-optimal solutions, which solve auxiliary optimization problems involving a smaller number of variables. For convex optimization problems having smooth solutions, we prove that the distance between the optimal solution and each sub-optimal approximation is related to the accuracy of the interpolation technique used within the MRF and analyze its relation with the performance of the proposed algorithm. Several numerical experiments confirm that our technique provides a computationally efficient strategy that allows the end user to treat both the optimizer and the objective function as black boxes throughout the optimization process.

math.OC↗

arXiv2018

Nonlinear stationary subdivision schemes that reproduce trigonometric functions

In this paper we define a family of nonlinear, stationary, interpolatory subdivision schemes with the capability of reproducing conic shapes including polynomials upto second order. Linear, non-stationary, subdivision schemes do also achieve this goal, but different conic sections require different refinement rules to guarantee exact reproduction. On the other hand, with our construction, exact reproduction of different conic shapes can be achieved using exactly the same nonlinear scheme. Convergence, stability, approximation and shape preservation properties of the new schemes are analyzed. In addition, the conditions to obtain $\mathcal{C}^1$ limit functions are also studied.

math.NA↗

arXiv2017

Implicit-Explicit WENO schemes for the equilibrium dispersive model of chromatography

Chromatographic processes can be modeled by nonlinear, convection-dominated partial differential equations, together with nonlinear relations: the adsorption isotherms. In this paper we consider the nonlinear equilibrium dispersive (ED) model with adsorption isotherms of Langmuir type. We show that very efficient, fully conservative, numerical schemes can be designed for this mode by exploiting the relation between the conserved variables of the model and the physical concentrations of the multi-component mixtures. We show that this relation is one to one and admits a smooth global inverse, which cannot be given explicitly but can be easily computed by using a convenient root finder. These results provide the necessary ingredients to implement fully conservative numerical schemes for the model considered. Implicit-Explicit (IMEX) techniques can be used in the convection-dominated regime in order to increase the efficiency of the numerical scheme. We propose a second order IMEX scheme, combining an explicit Weighted-Essentially-non-Oscillatory discretization of the convective fluxes with an implicit treatment of the diffusive term, in order to illustrate the numerical issues involved in the application of IMEX techniques to this model. Through a series of numerical experiments, we show that the scheme provides accurate numerical solutions which capture the sharp discontinuities present in the chromatographic fronts, with the same stability restrictions as in the purely hyperbolic case.

math.NA↗

arXiv2005

The Explicit Simplified Interface Method for compressible multicomponent flows

This paper concerns the numerical approximation of the Euler equations for multicomponent flows. A numerical method is proposed to reduce spurious oscillations that classically occur around material interfaces. It is based on the "Explicit Simplified Interface Method" (ESIM), previously developed in the linear case of acoustics with stationary interfaces (2001, J. Comput. Phys. 168, pp.~227-248). This technique amounts to a higher order extension of the "Ghost Fluid Method" introduced in Euler multicomponent flows (1999, J. Comput. Phys. 152, pp. 457-492). The ESIM is coupled to sophisticated shock-capturing schemes for time-marching, and to level-sets for tracking material interfaces. Jump conditions satisfied by the exact solution and by its spatial derivative are incorporated in numerical schemes, ensuring a subcell resolution of material interfaces inside the meshing. Numerical experiments show the efficiency of the method for rich-structured flows.

physics.class-ph↗