{"title":"Experiments with sparse Cholesky using a sequential task-flow implementation","authors":"I. Duff, J. Hogg, Florent Lopez","doi":"10.3934/NACO.2018014","DOIUrl":"https://doi.org/10.3934/NACO.2018014","url":null,"abstract":"We describe the development of a prototype code for the solution of large sparse symmetric positive definite systems that is efficient on parallel architectures. We implement a DAG-based Cholesky factorization that offers good performance and scalability on multicore architectures. Our approach uses a runtime system to execute the DAG. The runtime system plays the role of a software layer between the application and the architecture and handles the management of task dependencies as well as the task scheduling. In this model, the application is expressed using a high-level API, independent of the hardware details, thus enabling portability across different architectures. Although widely used in dense linear algebra, this approach is nevertheless challenging for sparse algorithms because of the irregularity and variable granularity of the DAGs arising in these systems. We assess the ability of two different Sequential Task Flow implementations to address this challenge: one implemented with the OpenMP standard, and the other with the modern runtime system StarPU. We compare these implementations to the state-of-the-art solver HSL_MA87 and demonstrate comparable performance on a multicore architecture.","PeriodicalId":407290,"journal":{"name":"Rutherford Appleton Laboratory Technical Reports","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116839030","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}
P. Amestoy, I. Duff, J. L’Excellent, Peter Plecháč
{"title":"PARASOL an Integrated Programming Environment for Parallel Sparse Matrix Solvers","authors":"P. Amestoy, I. Duff, J. L’Excellent, Peter Plecháč","doi":"10.1007/978-1-4615-4873-7_9","DOIUrl":"https://doi.org/10.1007/978-1-4615-4873-7_9","url":null,"abstract":"","PeriodicalId":407290,"journal":{"name":"Rutherford Appleton Laboratory Technical Reports","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116947580","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}
{"title":"Sparse system solution and the HSL Library","authors":"I. Duff","doi":"10.1142/9789812709356_0005","DOIUrl":"https://doi.org/10.1142/9789812709356_0005","url":null,"abstract":"We consider the solution of large sparse systems, sketch their ubiquity, and briefly describe some of the algorithms used to solve these systems. The HSL mathematical software library started life in 1963 as the Harwell Subroutine Library making it one of the oldest such libraries. The main strengths of the Library lie in packages for large scale system solution. It is particularly strong in direct methods for sparse matrices and optimization. The Library has been used worldwide by a wide range of industries. We briefly discuss the history of the library and its organization and contents. We discuss the evolution of some of our current packages and the efforts to ensure reliability, robustness, and efficiency. We describe in some detail the functionality of one of our most popular sparse direct codes.","PeriodicalId":407290,"journal":{"name":"Rutherford Appleton Laboratory Technical Reports","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125323783","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}
{"title":"Combinatorial problems in solving linear systems","authors":"I. Duff, B. Uçar","doi":"10.1201/b11644-3","DOIUrl":"https://doi.org/10.1201/b11644-3","url":null,"abstract":"Numerical linear algebra and combinatorial optimization are vast subjects; as is their interaction. In virtually all cases there should be a notion of sparsity for a combinatorial problem to arise. Sparse matrices therefore form the basis of the interaction of these two seemingly disparate subjects. As the core of many of today's numerical linear algebra computations consists of the solution of sparse linear system by direct or iterative methods, we survey some combinatorial problems, ideas, and algorithms relating to these computations. On the direct methods side, we discuss issues such as matrix ordering; bipartite matching and matrix scaling for better pivoting; task assignment and scheduling for parallel multifrontal solvers. On the iterative method side, we discuss preconditioning techniques including incomplete factorization preconditioners, support graph preconditioners, and algebraic multigrid. In a separate part, we discuss the block triangular form of sparse matrices.","PeriodicalId":407290,"journal":{"name":"Rutherford Appleton Laboratory Technical Reports","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130456113","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}
{"title":"MA62 - a frontal code for sparse positive definite symmetric systems from finite element applications","authors":"I. S. Duff, Jennifer A. Scott","doi":"10.4203/csets.1.1","DOIUrl":"https://doi.org/10.4203/csets.1.1","url":null,"abstract":"","PeriodicalId":407290,"journal":{"name":"Rutherford Appleton Laboratory Technical Reports","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114451581","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}