Multilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations
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Wave phenomena manifest in nature as electromagnetic waves, acoustic waves, and gravitational waves among others.Their descriptions as partial differential equations in electromagnetics, acoustics, and fluid dynamics are ubiquitous in science and engineeri ...
This paper examines the minimization of the cost for an expected random production output, given an assembly of finished goods from two random inputs, matched in two categories. We describe the optimal input portfolio, first using the standard normal appro ...
Isogeometric analysis (IGA) was introduced to integrate methods for analysis and computer-aided design (CAD) into a unified process. High-quality parameterization of a physical domain plays a crucial role in IGA. However, obtaining high-quality parameteriz ...
Let T be a measure-preserving Zℓ-action on the probability space (X,B,μ), let q1,…,qm:R→Rℓ be vector polynomials, and let f0,…,fm∈L∞(X). For any ϵ>0 and multicorrelation sequences of the form α(n)=∫Xf0⋅T⌊q1(n)⌋f1⋯T⌊qm(n)⌋fmdμ we show that there exis ...
We present a novel method for isogeometric analysis (IGA) to directly work on geometries constructed by Boolean operations including difference (i.e., trimming), union, and intersection. Particularly, this work focuses on the union operation, which involve ...
Semi-discrete optimal transport problems, which evaluate the Wasserstein distance between a discrete and a generic (possibly non-discrete) probability measure, are believed to be computationally hard. Even though such problems are ubiquitous in statistics, ...
A decomposition of multicorrelation sequences for commuting transformations along primes, Discrete Analysis 2021:4, 27 pp. Szemerédi's theorem asserts that for every positive integer k and every δ>0 there exists n such that every subset of ${1, ...
We present the fabrication of 570-mu m-thick millimeter-sized soda-lime-silicate float-glass blocks with a 1-mu m-thick AlN thin-film piezoelectric transducer sandwiched between thin metallic electrodes and deposited on the top surface. The electromechanic ...
We present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, which we call random mesh FEM (RM-FEM). Our methodology allows to introduce a pr ...
The matrix formation associated to high-order discretizations is known to be numerically demanding. Based on the existing procedure of interpolation and lookup, we design a multiscale assembly procedure to reduce the exorbitant assembly time in the context ...