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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 ...
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 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 ...
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 ...
Fluid flow in porous media is a multiscale process where the effective dynamics, which is often the goal of a computation, depends strongly on the porous micro structure. Resolving the micro structure in the whole porous medium can, however, be prohibitive ...
INTERNODES is a general method to deal with non-conforming discretizations of second order partial differential equations on regions partitioned into two or several subdomains. It exploits two intergrid interpolation operators, one for transfering the Diri ...
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 ...
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 ...
We propose a novel approach for smoothing on surfaces. More precisely, we aim at estimating functions lying on a surface, starting from noisy and discrete measurements. The surface is represented by NURBS, which are geometrical representations commonly use ...
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 ...
