Optimal control for Partial Differential Equations
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We propose a strategy for the systematic construction of the mimetic inner products on cochain spaces for the numerical approximation of partial differential equations on unstructured polygonal and polyhedral meshes. The mimetic inner products are locally ...
We prove that when a class of partial differential equations, generalized from the cable equation, is defined on tree graphs and the inputs are restricted to a spatially discrete, well chosen set of points, the Green's function (GF) formalism can be rewrit ...
The influence of a reflecting surface on the optical bistability in a nanoantenna array is investigated theoretically. The optical response of the array is modeled using a surface integral equation method developed for periodic structures, and the descript ...
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 project we numerically simulate electrophysiological models for cardiac applications by means of Isogeometric Analysis. Specifically, we aim at understanding the advantages of using high order continuous NURBS (Non-UniformRational B-Splines) basis ...
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 ...
A general framework to combine numerical homogenization and reduced-order modelling techniques for partial differential equations (PDEs) with multiple scales is described. Numerical homogenization methods are usually efficient to approximate the effective ...
Nonlinear modeling of coaxial microhelicopters is studied. All equations are derived using a Lagrangian approach and simplified aerodynamics assumptions so that all parameters have a physical meaning; there is no “black box.” The model is constructed with ...
This paper is concerned with the solution of heterogeneous problems by the interface control domain decomposition (ICDD) method, a strategy introduced for the solution of partial differential equations in computational domains partitioned into subdomains t ...
