AN IMPROVED MAC METHOD (SIMAC) FOR UNSTEADY HIGH-REYNOLDS FREE SURFACE FLOWS

A modified MAC method (SIMAC; semi-implicit marker and cell) is proposed which accurately treats unsteady high-Reynolds free surface problems. SIMAC solves the Navier–Stokes equations in primitive variables on a non-uniform staggered Cartesian grid by means of a finite difference scheme. The convective term is treated explicitly by employing a second-order upwind scheme in space (HLPA) and the Adams–Bashforth technique in time. The diffusive part is solved by means of the implicit approximate factorization technique. A multigrid technique based on the additive correction strategy is employed to solve the Poisson equation for the pressure. Finally, the free surface treatment is carried out using massless particles which divide the domain of integration into full and empty cells as in a standard MAC method. The algorithm is used for the analysis of large-amplitude water sloshing in rectangular unbaffled and baffled containers. Experimental tests have been carried out in order to validate the algorithm. Numerical results satisfactorily agree with experimental data for the whole range of filing conditions analysed here. © 1997 by John Wiley & Sons, Ltd.     

Alternatives for parallel Krylov subspace basis computation

Numerical methods related to Krylov subspaces are widely used in large sparse numerical linear algebra. Vectors in these subspaces are manipulated via their representation onto orthonormal bases. Nowadays, on serial computers, the method of Arnoldi is considered as a reliable technique for constructing such bases. However, although easily parallelizable, this technique is not as scalable as expected for communications. In this work we examine alternative methods aimed at overcoming this drawback. Since they retrieve upon completion the same information as Arnoldi's algorithm does, they enable us to design a wide family of stable and scalable Krylov approximation methods for various parallel environments. We present timing results obtained from their implementation on two distributed-memory multiprocessor supercomputers: the Intel Paragon and the IBM Scalable POWERparallel SP2. © 1997 John Wiley & Sons, Ltd.     

有限域上n元n次方程只有零解的充要条件

本文研究了有限域上只有零解的n元n次方程的结构问题.利用对有限域上不可约多元多项式在其扩域中的分解特征的刻画,结合Chevalley定理,得到了有限域上n元n次方程只有零解的一个充要条件,并给出这类方程的一些新的具体构造.     

A regularized nonnegative canonical polyadic decomposition algorithm with preprocessing for 3D fluorescence spectroscopy

We consider blind source separation in chemical analysis focussing on the 3D fluorescence spectroscopy framework. We present an alternative method to process the Fluorescence Excitation‐Emission Matrices (FEEM): first, a preprocessing is applied to eliminate the Raman and Rayleigh scattering peaks that clutter the FEEM. To improve its robustness versus possible improper settings, we suggest to associate the classical Zepp's method with a morphological image filtering technique. Then, in the second stage, the Canonical Polyadic (CP or Candecomp/Parafac) decomposition of a nonnegative three‐way array has to be computed. In the fluorescence spectroscopy context, the constituent vectors of the loading matrices should be nonnegative (since standing for spectra and concentrations). Thus, we suggest a new nonnegative third order CP decomposition algorithm (NNCP) based on a nonlinear conjugate gradient optimization algorithm with regularization terms and periodic restarts. Computer simulations performed on real experimental data are provided to enlighten the effectiveness and robustness of the whole processing chain and to validate the approach. Copyright © 2015 John Wiley & Sons, Ltd.     

Commutation of Geometry-Grids and Fast Discrete PDE Eigen-Solver GPA

A geometric intrinsic pre-processing algorithm(GPA for short) for solving largescale discrete mathematical-physical PDE in 2-D and 3-D case has been presented by Sun(in 2022–2023). Different from traditional preconditioning, the authors apply the intrinsic geometric invariance, the Grid matrix G and the discrete PDE mass matrix B,stiff matrix A satisfies commutative operator BG = GB and AG = GA, where G satisfies G^m= I, m << dim(G). A large scale system solvers can be replaced t...     

Efficient algorithms for computing rank-revealing factorizations on a GPU

Standard rank-revealing factorizations such as the singular value decomposition (SVD) and column pivoted QR factorization are challenging to implement efficiently on a GPU. A major difficulty in this regard is the inability of standard algorithms to cast most operations in terms of the Level-3 BLAS. This article presents two alternative algorithms for computing a rank-revealing factorization of the form $\mathsf{A}=\mathsf{U}\mathsf{T}{\mathsf{V}}^{\ast }$, where $\mathsf{U}$ and $\mathsf{V}$ are orthogonal and $\mathsf{T}$ is trapezoidal (or triangular if $\mathsf{A}$ is square). Both algorithms use randomized projection techniques to cast most of the flops in terms of matrix-matrix multiplication, which is exceptionally efficient on the GPU. Numerical experiments illustrate that these algorithms achieve significant acceleration over finely tuned GPU implementations of the SVD while providing low rank approximation errors close to that of the SVD.     

An Algebraic Multigrid-Based Physical Factorization Preconditioner for the Multi-Group Radiation Diffusion Equations in Three Dimensions

The paper investigates the robustness and parallel scaling properties of a novel physical factorization preconditioner with algebraic multigrid subsolves in the iterative solution of a cell-centered finite volume discretization of the three-dimensional multi-group radiation diffusion equations. The key idea is to take advantage of a particular kind of block factorization of the resulting system matrix and approximate the left-hand block matrix selectively spurred by parallel processing considerations. The spectral property of the preconditioned matrix is then analyzed. The practical strategy is considered sequentially and in parallel. Finally, numerical results illustrate the numerical robustness, computational efficiency and parallel strong and weak scalabilities over the real-world structured and unstructured coupled problems, showing its competitiveness with many existing block preconditioners.