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In this paper we provide a general framework for model reduction methods applied to fluid flow in porous media. Using reduced basis and numerical homogenization techniques we show that the complexity of the numerical approximation of Stokes flow in heterog ...
This thesis explores two aspects of the renormalization group (RG) in quantum field theory (QFT). In the first part we study the structure of RG flows in general Poincaré-invariant, unitary QFTs, and in particular the irreversibility properties and the rel ...
We propose two different improvements of reduced basis (RB) methods to enable the efficient and accurate evaluation of an output functional based on the numerical solution of parametrized partial differential equations with a possibly high-dimensional para ...
A review is presented of the most effective methods for the computation of Sommerfeld integral tails. Such integrals, which are often oscillatory, singular and divergent, commonly arise in layered media Green functions. The mathematical foundations of vari ...
A fully discrete a priori analysis of the finite element heterogeneous multiscale method introduced in [A. Abdulle, M. Grote, and C. Stohrer, Multiscale Model. Simul., 12, 2014, pp. 1135-1166] for the wave equation with highly oscillatory coefficients over ...
In this paper we give a survey on various multiscale methods for the numerical solution of second order hyperbolic equations in highly heterogenous media. We concentrate on the wave equation and distinguish between two classes of applications. First we dis ...
In this paper we develop and analyze a multilevel weighted reduced basis method for solving stochastic optimal control problems constrained by Stokes equations. We prove the analytic regularity of the optimal solution in the probability space under certain ...
We numerically study the resistive method for the numerical approximation of elliptic PDEs. In particular we focus on the resistive method for weakly setting solution values in specific subdomains or interfaces in the domain. ...
The objective of this thesis is to develop efficient numerical schemes to successfully tackle problems arising from the study of groundwater flows in a porous saturated medium; we deal therefore with partial differential equations(PDE) having random coeffi ...
We investigate a finite element approximation of an initial boundary value problem associated with parabolic Partial Differential Equations endowed with mixed time varying boundary conditions, switching from essential to natural and vice versa. The switchi ...