Related papers: A Scheme to Numerically Evolve Data for the Confor…

In the theory and practice of inverse problems for partial differential equations (PDEs) much attention is paid to the problem of the identification of coefficients from some additional information. This work deals with the problem of…

The numerical evaluation of statistics plays a crucial role in statistical physics and its applied fields. It is possible to evaluate the statistics for a stochastic differential equation with Gaussian white noise via the corresponding…

We consider the problem of discrete-time signal denoising, focusing on a specific family of non-linear convolution-type estimators. Each such estimator is associated with a time-invariant filter which is obtained adaptively, by solving a…

Abbreviated Abstract: The objective of Evolutionary Computation is to solve practical problems (e.g. optimization, data mining) by simulating the mechanisms of natural evolution. This thesis addresses several topics related to adaptation…

We present a collection of algorithms which utilize dimensional reduction to perform mesh refinement and study possibly singular solutions of time-dependent partial differential equations. The algorithms are inspired by constructions used…

We develop a novel iterative algorithm for locally optimal experimental design under constraints, like budget or performance constraints. It is an adaptive discretization algorithm. In every iteration, a discretized version of the…

This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…

We analyse a numerical scheme for a system arising from a novel description of the standard elastic--perfectly plastic response. The elastic--perfectly plastic response is described via rate-type equations that do not make use of the…

In this paper, we combine the operator splitting methodology for abstract evolution equations with that of stochastic methods for large-scale optimization problems. The combination results in a randomized splitting scheme, which in a given…

Physical laws governing population dynamics are generally expressed as differential equations. Research in recent decades has incorporated fractional-order (non-integer) derivatives into differential models of natural phenomena, such as…

In this paper, we present a rigorous proof of the convergence of first order and second order exponential time differencing (ETD) schemes for solving the nonlocal Cahn-Hilliard (NCH) equation. The spatial discretization employs the Fourier…

We propose an accurate data-driven numerical scheme to solve Stochastic Differential Equations (SDEs), by taking large time steps. The SDE discretization is built up by means of a polynomial chaos expansion method, on the basis of…

We present a general abstract framework for the systematic numerical approximation of dissipative evolution problems. The approach is based on rewriting the evolution problem in a particular form that complies with an underlying energy or…

Many differential equations with physical backgrounds are described as gradient systems, which are evolution equations driven by the gradient of some functionals, and such problems have energy conservation or dissipation properties. For…

We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial…

This paper is part of a program to combine a staggered time and staggered spatial discretization of continuum wave equations so that important properties of the continuum that are proved using vector calculus can be proven in an analogous…

On the basis of additive schemes (splitting schemes) we construct efficient numerical algorithms to solve approximately the initial-boundary value problems for systems of time-dependent partial differential equations (PDEs). In many applied…

This paper deals with the Darcy-Forchheimer problem with two kinds of boundary conditions. We discretize the system by using the finite element methods and we propose two iterative schemes to solve the discrete problems. The well-posedness…

Conformal prediction has emerged as a widely used framework for constructing valid prediction sets in classification and regression tasks. In this work, we extend the split conformal prediction framework to hierarchical classification,…

Many algorithms have been developed for enumerating various combinatorial objects in time exponentially less than the number of objects. Two common classes of algorithms are dynamic programming and the transfer matrix method. This paper…