MATHICSE Technical Report : Dimensionality reduction of parameter-dependent problems through proper orthogonal decomposition
Graph Chatbot
Chat with Graph Search
Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.
DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.
Stochastic models that account for sudden, unforeseeable events play a crucial role in many different fields such as finance, economics, biology, chemistry, physics and so on. That kind of stochastic problems can be modeled by stochastic differential equat ...
We provide a mathematical analysis and a numerical framework for magnetoacoustic tomography with magnetic induction. The imaging problem is to reconstruct the conductivity distribution of biological tissue from measurements of the Lorentz force induced tis ...
In this work, we apply a Matrix version of the so-called Discrete Empirical Interpolation (MDEIM) for the efficient reduction of nonaffine parametrized systems arising from the discretization of linear partial differential equations. Dealing with affinely ...
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 work we develop an adaptive and reduced computational algorithm based on dimension-adaptive sparse grid approximation and reduced basis methods for solving highdimensional uncertainty quantification (UQ) problems. In order to tackle the computation ...
In this work, we apply a Matrix version of the so-called Discrete Empirical Interpolation (MDEIM) for the efficient reduction of nonaffine parametrized systems arising from the discretization of linear partial differential equations. Dealing with affinely ...
We provide a mathematical analysis and a numerical framework for Lorentz force electrical conductivity imaging. Ultrasonic vibration of a tissue in the presence of a static magnetic field induces an electrical current by the Lorentz force. This current can ...
In the following work we apply the boundary element method to two-phase flows in shallow microchannels, where one phase is dispersed and does not wet the channel walls. These kinds of flows are often encountered in microfluidic Lab-On-A-Chip devices and ch ...
Numerical methods for partial differential equations with multiple scales that combine numerical homogenization methods with reduced order modeling techniques are discussed. These numerical methods can be applied to a variety of problems including multisca ...
Within a deterministic framework, it is well known that n-term wavelet approximation rates of functions can be deduced from their Besov regularity. We use this principle to determine approximation rates for symmetric-α-stable (SαS) stochastic processes. Fi ...
