MATHICSE Technical Report : Low-rank updates and a divideand- conquer method for linear matrix equations
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In Control System Theory, the study of continuous-time, finite dimensional, underdetermined systems of ordinary differential equations is an important topic. Classification of systems in different categories is a natural initial step to the analysis of a g ...
We consider the approximate computation of spectral projectors for symmetric banded matrices. While this problem has received considerable attention, especially in the context of linear scaling electronic structure methods, the presence of small relative s ...
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A definition of bivariate matrix functions is introduced and some theoretical as well as algorithmic aspects are analyzed. It is shown that our framework naturally extends the usual notion of (univariate) matrix functions and allows to unify existing resul ...
In this project report, we first present the application of the finite elements method to the numerical approximation of elliptic and parabolic PDEs over two-dimensional domains. We then consider the theory and numerical approximation of optimal control pr ...
We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation with random data, where the random coefficient is parametrized by means of a countable sequence of terms in a ...
This paper is concerned with the solution of heterogeneous problems by the interface control domain decomposition (ICDD) method, a strategy introduced for the solution of partial differential equations in computational domains partitioned into subdomains t ...
We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation (PDE) with random data, where the random coefficient is parametrized by means of a countable sequence of term ...
We show that concurrent atomistic/continuum displacement-coupling methods are inherently unstable in the context of fully dynamic problems at finite temperature. The fundamental origin of the instability is the displacement coupling of two material descrip ...
In this work we present a stable proper orthogonal decomposition (POD)-Galerkin approximation for parametrized steady incompressible Navier-Stokes equations with low Reynolds number. Supremizers solutions are added to the reduced velocity space in order to ...