Two-Level Discretization Techniques For Ground State Computations Of Bose-Einstein Condensates
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In many signal processing, machine learning and computer vision applications, one often has to deal with high dimensional and big datasets such as images, videos, web content, etc. The data can come in various forms, such as univariate or multivariate time ...
We develop an analytical formulation to calculate the induced resonance frequency shifts of an electrostatically actuated torsional microsensor due to an added bio-mass (E. coli). Based on a lumped-parameter model, we investigate the static and the linear ...
In this thesis, we consider the numerical approximation of high order geometric Partial Differential Equations (PDEs). We first consider high order PDEs defined on surfaces in the 3D space that are represented by single-patch tensor product NURBS. Then, we ...
A reduced basis Darcy-Stokes finite element heterogeneous multiscale method (RB-DS-FE-HMM) is proposed for the Stokes problem in porous media. The multiscale method is based on the Darcy-Stokes finite element heterogeneous multiscale method (DS-FE-HMM) int ...
In this paper, we introduce and analyze a new low-rank multilevel strategy for the solution of random diffusion problems. Using a standard stochastic collocation scheme, we first approximate the infinite dimensional random problem by a deterministic parame ...
Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications. In this work, we study the low-rank approximability of solutions to linear systems and eigenvalue p ...
Matrix equations of the kind A(1)X(2)+A(0)X+A(-1)=X, where both the matrix coefficients and the unknown are semi-infinite matrices belonging to a Banach algebra, are considered. These equations, where coefficients are quasi-Toeplitz matrices, are encounter ...
In this work we extend to the Stokes problem the Discontinuous Galerkin Reduced Basis Element (DGRBE) method introduced in Antonietti et al. (2015). By this method we aim at reducing the computational cost for the approximation of a parametrized Stokes pro ...
The numerical solution of partial differential equations (PDEs) depending on para- metrized or random input data is computationally intensive. Reduced order modeling techniques, such as the reduced basis methods, have been developed to alleviate this compu ...
The focus of this thesis is on developing efficient algorithms for two important problems arising in model reduction, estimation of the smallest eigenvalue for a parameter-dependent Hermitian matrix and solving large-scale linear matrix equations, by extra ...