IGA-based Multi-Index Stochastic Collocation for random PDEs on arbitrary domains

This paper proposes an extension of the Multi-Index Stochastic Collocation (MISC) method for forward uncertainty quantification (UQ) problems in computational domains of shape other than a square or cube, by exploiting isogeometric analysis (IGA) techniques. Introducing IGA solvers to the MISC algorithm is very natural since they are tensor-based PDE solvers, which are precisely what is required by the MISC machinery. Moreover, the combination-technique formulation of MISC allows the straight-forward reuse of existing implementations of IGA solvers. We present numerical results to showcase the effectiveness of the proposed approach.Comment: version 3, version after revisio

Multi-index Stochastic Collocation convergence rates for random PDEs with parametric regularity

We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation (PDEs) with random data, where the random coefficient is parametrized by means of a countable sequence of terms in a suitable expansion. MISC is a combination technique based on mixed differences of spatial approximations and quadratures over the space of random data and, naturally, the error analysis uses the joint regularity of the solution with respect to both the variables in the physical domain and parametric variables. In MISC, the number of problem solutions performed at each discretization level is not determined by balancing the spatial and stochastic components of the error, but rather by suitably extending the knapsack-problem approach employed in the construction of the quasi-optimal sparse-grids and Multi-index Monte Carlo methods. We use a greedy optimization procedure to select the most effective mixed differences to include in the MISC estimator. We apply our theoretical estimates to a linear elliptic PDEs in which the log-diffusion coefficient is modeled as a random field, with a covariance similar to a Mat\'ern model, whose realizations have spatial regularity determined by a scalar parameter. We conduct a complexity analysis based on a summability argument showing algebraic rates of convergence with respect to the overall computational work. The rate of convergence depends on the smoothness parameter, the physical dimensionality and the efficiency of the linear solver. Numerical experiments show the effectiveness of MISC in this infinite-dimensional setting compared with the Multi-index Monte Carlo method and compare the convergence rate against the rates predicted in our theoretical analysis

Psychiatric Indications for the Use of Contraceptives

A couple sits together and reads a pamphlet near the Cupples House on SLU's main campus. (August 27, 1990) [Misc slides-stock book folder, page 1990-Aug

Misc. Pub. 91-1

I submit herewith the annual report of the Agricultural and Forestry Experiment Station, School of Agriculture and Land Resources Management, University of Alaska Fairbanks, for the period ending December 31,1990. This is done in accordance with an act of the Congress, approved March 2,1887, entitled "An act to establish Agricultural Experiment Stations, in connection with the Agricultural Colleges established in the several states under the provisions of an act approved July 2,1862, and under the acts supplementary thereto," and also of the act of the Alaska Territorial Legislature, approved March 12,1935, accepting the provisions of the act of Congress. James V. Drew, DirectorStatement of Purpose -- Plant and Animal Sciences -- Forest Sciences -- Resources Management -- Financial Statement -- Publications - Staf

Misc. Pub. 99-6

Sausages, one of the oldest forms of processed food, are a means of using and preserving animal trimmings. The hot dog is a specialized sausage. It originated in Germany where it was named “dachshund” sausage because it looked like the popular badger (dachs) hound (hund). The U.S. hot dog originated at the Polo Grounds in New York. Vendors hawked dachshund sausages in buns while a sports cartoonist sketched a barking dachshund nestled warmly in a bun. He labeled the cartoon “hot dog”. Today the hot dog enjoys popularity throughout the world

Chapman-Enskog expansion about nonequilibrium states: the sheared granular fluid

The Chapman-Enskog method of solution of kinetic equations, such as the Boltzmann equation, is based on an expansion in gradients of the deviations fo the hydrodynamic fields from a uniform reference state (e.g., local equilibrium). This paper presents an extension of the method so as to allow for expansions about \emph{arbitrary}, far-from equilibrium reference states. The primary result is a set of hydrodynamic equations for studying variations from the arbitrary reference state which, unlike the usual Navier-Stokes hydrodynamics, does not restrict the reference state in any way. The method is illustrated by application to a sheared granular gas which cannot be studied using the usual Navier-Stokes hydrodynamics.Comment: 23 pages, no figures. Submited to PRE Replaced to correct misc. errors Replaced to correct misc. errors, make notation more consistant, extend discussio