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In this paper we review various numerical homogenization methods for monotone parabolic problems with multiple scales. The spatial discretisation is based on finite element methods and the multiscale strategy relies on the heterogeneous multiscale method. ...
A new decomposition optimization algorithm, called path-following gradient-based decomposition, is proposed to solve separable convex optimization problems. Unlike path-following Newton methods considered in the literature, this algorithm does not require ...
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 paper is concerned with the numerical solution of symmetric large-scale Lyapunov equations with low-rank right-hand sides and coefficient matrices depending on a parameter. Specifically, we consider the situation when the parameter dependence is suffi ...
Numerical methods for parabolic homogenization problems combining finite element methods (FEMs) in space with Runge-Kutta methods in time are proposed. The space discretization is based on the coupling of macro and micro finite element methods following th ...
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 parareal algorithm seeks to extract parallelism in the time-integration direction of time-dependent differential equations. While it has been applied with success to a wide range of problems, it suffers from some stability issues when applied to non-di ...
This work is concerned with the numerical solution of large-scale linear matrix equations A1XB1T++AKXBKT=C. The most straightforward approach computes XRmxn from the solution of an mn x mn linear system, typically limiting the feasible values of m,n to a f ...
This lecture describes the following topics: • Dynamic Models - Conservation of Mass (Concentration Measurements) - Conservation of Energy (Calorimetry) - Beer’s Law (Spectroscop ...
Power grid analysis is a challenging problem for mod- ern integrated circuits. For 3-D systems fabricated using stacked tiers with TSVs, traditional power grid analysis methods for pla- nar (2-D) circuits do not demonstrate the same performance. An efficie ...