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In this project report, we first present the application of the finite elements method to the numerical approximation of elliptic and parabolic PDEs over two-dimensional domains. We then consider the theory and numerical approximation of optimal control pr ...
Several computational challenges arise when evaluating the failure probability of a given system in the context of risk prediction or reliability analysis. When the dimension of the uncertainties becomes high, well established direct numerical methods can ...
We consider elliptic PDEs (partial differential equations) in the framework of isogeometric analysis, i.e., we treat the physical domain by means of a B-spline or NURBS mapping which we assume to be regular. The numerical solution of the PDE is computed by ...
We consider a method to efficiently evaluate in a real-time context an output based on the numerical solution of a partial differential equation depending on a large number of parameters. We state a result allowing to improve the computational performance ...
A new method for solving numerically stochastic partial differential equations (SPDEs) with multiple scales is presented. The method combines a spectral method with the heterogeneous multiscale method (HMM) presented in [W. E, D. Liu, E. Vanden-Eijnden, An ...
In this work we propose and analyze a weighted reduced basis method to solve elliptic partial differential equations (PDEs) with random input data. The PDEs are first transformed into a weighted parametric elliptic problem depending on a finite number of p ...
In this paper we present a compact review on the mostly used techniques for computational reduction in numerical approximation of partial differential equations. We highlight the common features of these techniques and provide a detailed presentation of th ...
The objective of this thesis is to develop reduced models for the numerical solution of optimal control, shape optimization and inverse problems. In all these cases suitable functionals of state variables have to be minimized. State variables are solutions ...
Every wave solver serving the computational study of waves meets a trade-off of two figures of merit—its computational speed and its accuracy. The use of Discontinuous Galerkin (DG) methods on graphical processing units (GPUs) significantly lowers the cost ...
The goal of this report is to study the method introduced by Adomian known as the Adomian Decomposition Method (ADM), which is used to find an approximate solution to nonlinear partial differential equations (PDEs) as a series expansion involving the recur ...