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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 ...
Finite elements methods (FEMs) with numerical integration play a central role in numerical homogenization methods for partial differential equations with multiple scales, as the effective data in a homogenization problem can only be recovered from a micros ...
We consider the numerical solution of second order Partial Differential Equations (PDEs) on lower dimensional manifolds, specifically on surfaces in three dimensional spaces. For the spatial approximation, we consider Isogeometric Analysis which facilitate ...
Isogeometric Analysis (IGA) is a computational methodology for the numerical approximation of Partial Differential Equations (PDEs). IGA is based on the isogeometric concept, for which the same basis functions, usually Non-Uniform Rational B-Splines (NURBS ...
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 ...
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 ...
This volume presents selected papers from the ninth International Conference on Spectral and High Order Methods (ICOSAHOM’12) conference that was held at Gammarth, Tunisia, during the week June 25–29, 2012. These selected papers were refereed by members of ...
The numerical solution of partial differential equations (PDEs) depending on para- metrized or random input data is computationally intensive. Reduced order modeling techniques, such as the reduced basis methods, have been developed to alleviate this compu ...
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 ...
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 ...