Siam Journal on Scientific and Statistical Computing最新文献_第3页

Practical Runge–Kutta Processes 实用龙格-库塔过程

Siam Journal on Scientific and Statistical Computing Pub Date : 1989-09-01 DOI: 10.1137/0910057

J. Dormand, P. Prince

引用次数: 55

A new order selection strategy for ordinary differential equation solvers 一种新的常微分方程解序选择策略

Siam Journal on Scientific and Statistical Computing Pub Date : 1989-09-01 DOI: 10.1137/0910061

P. Tischer

引用次数: 1

Numerical solution of boundary value problems in differential-algebraic systems 微分代数系统边值问题的数值解

Siam Journal on Scientific and Statistical Computing Pub Date : 1989-09-01 DOI: 10.1137/0910053

K. Clark, L. Petzold

{"title":"Numerical solution of boundary value problems in differential-algebraic systems","authors":"K. Clark, L. Petzold","doi":"10.1137/0910053","DOIUrl":"https://doi.org/10.1137/0910053","url":null,"abstract":"This paper extends the theory of shooting and finite-difference methods for linear boundary value problems (BVPs) in ordinary differential equations (ODEs) to BVPs in differential-algebraic equations (DAEs) of the form [ begin{gathered} E(t)mathcal{Y}'(t) + F(t)mathcal{Y}(t) = f(t),t in [a,b], hfill B_a mathcal{Y}(a) + B_b mathcal{Y} (b) = beta , hfill end{gathered} ] where $E( cdot )$, $F( cdot )$, and $f( cdot )$ are sufficiently smooth and the DAE initial value problem (IVP) is solvable. $E(t)$ may be singular on $[a,b]$ with variable rank, and the DAE may have an index that is larger than one. When $E(t)$ is nonsingular, the singular theory reduces to the standard theory for ODEs. The convergence results for backward differentiation formulas and Runge–Kutta methods for several classes of DAE IVPs are applied to obtain convergence of the corresponding shooting and finite-difference methods for these DAE boundary value problems. These methods can be implemented directly without having to (1) regularize the system to a lower index DAE or ODE or (2) convert the system to a particular canonical structure. Finally, some numerical experiments that illustrate these results are presented.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115452504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 36

Efficient split linear multistep methods for stiff ordinary differential equations 求解刚性常微分方程的有效分段线性多步方法

Siam Journal on Scientific and Statistical Computing Pub Date : 1989-09-01 DOI: 10.1137/0910058

D. Voss, M. Casper

引用次数: 20

A Riemann solver for a two-phase multicomponent process 两相多组分过程的黎曼解算器

Siam Journal on Scientific and Statistical Computing Pub Date : 1989-09-01 DOI: 10.1137/0910050

T. Johansen, A. Tveito, R. Winther

引用次数: 27

Computational structure of the N-body problem n体问题的计算结构

Siam Journal on Scientific and Statistical Computing Pub Date : 1989-07-01 DOI: 10.1137/0910048

J. Katzenelson

{"title":"Computational structure of the N-body problem","authors":"J. Katzenelson","doi":"10.1137/0910048","DOIUrl":"https://doi.org/10.1137/0910048","url":null,"abstract":"This work considers tree algorithms for the N-body problem where the number of particles is on the order of a million. The main concern of this work is the organization and performance of these computations on parallel computers.This work introduces a formulation of the N-body problem as a set of recursive equations based on a few elementary functions. It is shown that both the algorithm of Barnes–Hut and that of Greengard–Rokhlin satisfy these equations using different elementary functions. The recursive formulation leads directly to a computational structure in the form of a pyramid-like graph, where each vertex is a process, and each arc a communication link.The pyramid is mapped to three different processor configurations: (1) a pyramid of processors corresponding to the processes pyramid graph; (2) a hypercube of processors, e.g., a connection-machine-like architecture; and (3) a rather small array, e.g., $2 times 2 times 2$, of processors faster than the ones considered in (1) and (2) above.The main conclusion is that simulations of this size can be performed on any of the three architectures in reasonable time. Approximately 24 seconds per timestep is the estimate for a million equally distributed particles using the Greengard-Rokhlin algorithm on the CM-2 connection machine. The smaller array of processors is quite competitive in performance.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128831600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 39

Spanning balanced trees in Boolean cubes 生成布尔立方体中的平衡树

Siam Journal on Scientific and Statistical Computing Pub Date : 1989-07-01 DOI: 10.1137/0910038

Ching-Tien Ho, S. Johnsson

{"title":"Spanning balanced trees in Boolean cubes","authors":"Ching-Tien Ho, S. Johnsson","doi":"10.1137/0910038","DOIUrl":"https://doi.org/10.1137/0910038","url":null,"abstract":"A Spanning Balancedn-tree (SBnT) in a Boolean n-cube is a spanning tree in which the root has fanout n, and all the subtrees of the root have $O({{2^n } / n})$ nodes. The number of tree edges in each dimension of the n-cube is of order $O({{2^n } / n})$. The spanning balanced n-tree allows for scheduling disciplines that realize lower bound (within a factor of two) one-to-all personalized communication, all-to-all broadcasting, and all-to-all personalized communication on a Boolean n-cube [C.-T. Ho and S. L. Johnsson, Proc. 1986 International Conference on Parallel Processing, pp. 640–648, IEEE Computer Society, 1986; Tech. Report YALEU/DCS/RR–483, May 1986], [S. L. Johnsson and C.-T. Ho, Tech. Report YALEU/DCS/RR–610, Dept. of Computer Science, Yale Univ., New Haven, CT, November 1987]. The improvement in data transfer time over the familiar binomial tree routing is a factor of ${n / 2}$ for concurrent communication on all ports and one-to-all personalized communication and all-to-all broadcasting. For all-to-all personalized communication on all ports concurrently, the improvement is of order $O(sqrt n )$. Distributed routing algorithms defining the spanning balanced n-tree are given. The balanced n-tree is not unique, and a few definitions of n-trees that are effectively edge-disjoint are provided. Some implementation issues are also discussed.Binary numbers obtained from each other through rotation form necklaces that are full if the period is equal to the length of the number; otherwise, they are degenerate. As an intermediary result, it is shown that the ratio between the number of degenerate necklaces and the total number of necklaces with l bits equal to one is at most ${4 / {(4 + n)}}$ for $1 leqq l < n$.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128649098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 36

A conservative adaptive method for flame propagation 一种火焰传播的保守自适应方法

Siam Journal on Scientific and Statistical Computing Pub Date : 1989-07-01 DOI: 10.1137/0910045

B. Larrouturou

引用次数: 11

Numerical determination of an emanating branch of Hopf bifurcation points in a two-parameter problem 双参数问题Hopf分岔点发散分支的数值确定

Siam Journal on Scientific and Statistical Computing Pub Date : 1989-07-01 DOI: 10.1137/0910041

D. Roose, B. D. Dier

引用次数: 34

Three-dimensional triangulations from local transformations 局部变换的三维三角剖分

Siam Journal on Scientific and Statistical Computing Pub Date : 1989-07-01 DOI: 10.1137/0910044

B. Joe

引用次数: 213