Sparse tensor product high dimensional finite elements for two-scale mixed problems

2021 ◽  
Vol 85 ◽  
pp. 42-56
Author(s):  
Van Tiep Chu ◽  
Viet Ha Hoang ◽  
Roktaek Lim
Keyword(s):  
Finite Elements ◽  
Tensor Product ◽  
High Dimensional ◽  
Mixed Problems

High-dimensional finite elements for multiscale Maxwell-type equations

2017 ◽  
Vol 38 (1) ◽  
pp. 227-270 ◽  
Author(s):  
Van Tiep Chu ◽  
Viet Ha Hoang
Keyword(s):  
Finite Elements ◽  
High Dimensional

First Instances of Univariate and Tensor-product Multivariate Generalized Expo-Rational Finite Elements

2011 ◽  
Author(s):  
Lubomir T. Dechevsky ◽  
Peter Zanaty ◽  
George Venkov ◽  
Ralitza Kovacheva ◽  
Vesela Pasheva
Keyword(s):  
Finite Elements ◽  
Tensor Product

scholarly journals Automated Generation and Symbolic Manipulation of Tensor Product Finite Elements

2016 ◽  
Vol 38 (5) ◽  
pp. S25-S47 ◽  
Author(s):  
A. T. T. McRae ◽  
G.-T. Bercea ◽  
L. Mitchell ◽  
D. A. Ham ◽  
C. J. Cotter
Keyword(s):  
Finite Elements ◽  
Tensor Product ◽  
Symbolic Manipulation ◽  
Automated Generation

scholarly journals Pointwise supercloseness of the displacement for tensor-product quadratic pentahedral finite elements

2012 ◽  
Vol 25 (10) ◽  
pp. 1458-1463 ◽  
Author(s):  
Jinghong Liu
Keyword(s):  
Finite Elements ◽  
Tensor Product

High dimensional finite elements for two-scale Maxwell wave equations

2020 ◽  
Vol 375 ◽  
pp. 112756
Author(s):  
Van Tiep Chu ◽  
Viet Ha Hoang
Keyword(s):  
Finite Elements ◽  
Wave Equations ◽  
High Dimensional

scholarly journals C1 finite elements on non-tensor-product 2d and 3d manifolds

2016 ◽  
Vol 272 ◽  
pp. 148-158 ◽  
Author(s):  
Thien Nguyen ◽  
Kȩstutis Karčiauskas ◽  
Jörg Peters
Keyword(s):  
Finite Elements ◽  
Tensor Product ◽  
2D And 3D

Modified SPR Technique for 3D Tensor-Product Block Finite Elements: A Computer-Based Test

2011 ◽  
Vol 101-102 ◽  
pp. 1190-1193
Author(s):  
Jing Hong Liu ◽  
De Cheng Yin
Keyword(s):  
Finite Elements ◽  
Boundary Conditions ◽  
Tensor Product ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Open Domain ◽  
Poisson Problem ◽  
Computer Based ◽  
Homogeneous Dirichlet Boundary Conditions

In this paper, the Poisson problem with homogeneous Dirichlet boundary conditions on the bounded open domain is considered and the superconvergence property of 3D tensor-product block finite elements is analyzed by using a computer-based test.

scholarly journals High Dimensional Finite Elements for Multiscale Wave Equations

2014 ◽  
Vol 12 (4) ◽  
pp. 1622-1666 ◽  
Author(s):  
Bingxing Xia ◽  
Viet Ha Hoang
Keyword(s):  
Finite Elements ◽  
Wave Equations ◽  
High Dimensional

scholarly journals An efficient high dimensional quantum Schur transform

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 122 ◽  
Author(s):  
Hari Krovi
Keyword(s):  
Fourier Transform ◽  
Representation Theory ◽  
Tensor Product ◽  
Unitary Operator ◽  
Group Representation ◽  
Quantum Algorithm ◽  
Unitary Groups ◽  
High Dimensional ◽  
Quantum Fourier Transform ◽  
Dual Algorithm

The Schur transform is a unitary operator that block diagonalizes the action of the symmetric and unitary groups on an n fold tensor product V⊗n of a vector space V of dimension d. Bacon, Chuang and Harrow [5] gave a quantum algorithm for this transform that is polynomial in n, d and log⁡ϵ−1, where ϵ is the precision. In a footnote in Harrow's thesis [18], a brief description of how to make the algorithm of [5] polynomial in log⁡d is given using the unitary group representation theory (however, this has not been explained in detail anywhere). In this article, we present a quantum algorithm for the Schur transform that is polynomial in n, log⁡d and log⁡ϵ−1 using a different approach. Specifically, we build this transform using the representation theory of the symmetric group and in this sense our technique can be considered a ''dual" algorithm to [5]. A novel feature of our algorithm is that we construct the quantum Fourier transform over the so called permutation modules, which could have other applications.

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