MATHICSE Technical Report : Dimensionality reduction of parameter-dependent problems through proper orthogonal decomposition
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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 ...
How should we present training examples to learners to teach them classification rules? This is a natural problem when training workers for crowdsourcing labeling tasks, and is also moti- vated by challenges in data-driven online educa- tion. We propose a ...
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 ...
Procedural modeling allows for the generation of innumerable variations of models from a parameterized, conditional or stochastic rule set. Due to the abstractness, complexity and stochastic nature of rule sets, it is often very difficult to have an unders ...
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 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 ...
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 ...
In this thesis we study the efficient implementation of the finite element method for the numerical solution of partial differential equations (PDE) on modern parallel computer archi- tectures, such as Cray and IBM supercomputers. The domain-decomposition ...
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 ...
The workshop has brought together experts in the broad field of partial differential equations with highly heterogeneous coefficients. Analysts and computational and applied mathematicians have shared results and ideas on a topic of considerable interest b ...