Numerical pancake droplets: from capturing to versatile microfluidics
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Multiscale differential equations arise in the modeling of many important problems in the science and engineering. Numerical solvers for such problems have been extensively studied in the deterministic case. Here, we discuss numerical methods for (mean-squ ...
The numerical analysis of a dynamic constrained optimization problem is presented. It consists of a global minimization problem that is coupled with a system of ordinary differential equations. The activation and the deactivation of inequality constraints ...
A large portion of software is used for numerical calculations in mathematics, physics and engineering applications. Among the things that make verification in this domain difficult is the quantification of numerical errors, such as roundoff errors and err ...
It is important to consider the microstructure of a material when studying the macroscopic mechanical properties. Although special equipments have been used for micromechanics study through experimental tests, it is limited by instruments and reproducibili ...
Among the efficient numerical methods based on atomistic models, the quasi-continuum (QC) method has attracted growing interest in recent years. The QC method was first developed for crystalline materials with Bravais lattice and was later extended to mult ...
A tomography-based methodology for the mass transport characterization of snow is presented. Five samples, characteristic for a wide range of seasonal snow, are considered. Their three-dimensional (3-D) geometrical representations are obtained by micro-com ...
Highly accurate and efficient cubatures based on the double exponential quadrature rules are presented for the computation of weakly singular integrals arising in Galerkin mixed potential integral equation formulations. Due to their unique ability to handl ...
Institute of Electrical and Electronics Engineers2012
Much attention has recently been devoted to the development of Stochastic Galerkin (SG) and Stochastic Collocation (SC) methods for uncertainty quantification. An open and relevant research topic is the comparison of these two methods. By introducing a sui ...
Engineers rely on efficient simulations that provide them with reliable data in order to make proper engineering design decisions. The purpose of this thesis is to design adaptive numerical methods for multiscale problems in this spirit. We consider ellipt ...