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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 ...
The numerical solution of partial differential equations on high-dimensional domains gives rise to computationally challenging linear systems. When using standard discretization techniques, the size of the linear system grows exponentially with the number ...
In this paper we develop theoretical analysis and numerical reconstruction techniques for the solution of an inverse boundary value problem dealing with the nonlinear, time-dependent monodomain equation, which models the evolution of the electric potential ...
Aquatic ecologists have recently employed dynamic models to estimate aquatic ecosystem metabolism. All approaches involve numerically solving a differential equation describing dissolved oxygen (DO) dynamics. Although the DO differential equation can be so ...
Association for the Sciences of Limnology and Oceanography2016
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 ...
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 ...
We consider the numerical approximation of geometric Partial Differential Equations (PDEs) defined on surfaces in the 3D space. In particular, we focus on the geometric PDEs deriving from the minimization of an energy functional by L2-gradient ow. We analy ...
In this article, the second-harmonic generation (SHG) from gold split-ring resonators is investigated using different theoretical methods, namely, Miller's rule, the nonlinear effective susceptibility method, and full-wave computation based on a surface in ...
Mathematical models involving partial differential equations (PDE) arise in numerous applications ranging from Natural Sciences and Engineering to Economics. Random and stochastic PDE models become very powerful (and sometimes unavoidable) extensions of de ...
We consider the numerical approximation of geometric Partial Differential Equations (PDEs) defined on surfaces in the 3D space. In particular, we focus on the geometric PDEs deriving from the minimization of an energy functional by L2L2-gradient flow. We a ...
