Results 1 
5 of
5
Amesos2 and Belos: Direct and iterative solvers for large sparse linear systems
 Scientific Programming
, 2012
"... Solvers for large sparse linear systems come in two categories: direct and iterative. Amesos2, a package in the Trilinos software project, provides direct methods, and Belos, another Trilinos package, provides iterative methods. Amesos2 offers a common interface to many different sparse matrix fact ..."
Abstract

Cited by 7 (6 self)
 Add to MetaCart
(Show Context)
Solvers for large sparse linear systems come in two categories: direct and iterative. Amesos2, a package in the Trilinos software project, provides direct methods, and Belos, another Trilinos package, provides iterative methods. Amesos2 offers a common interface to many different sparse matrix factorization codes, and can handle any implementation of sparse matrices and vectors, via an easytoextend C++ traits interface. It can also factor matrices whose entries have arbitrary “Scalar ” type, enabling extendedprecision and mixedprecision algorithms. Belos includes many different iterative methods for solving large sparse linear systems and leastsquares problems. Unlike competing iterative solver libraries, Belos completely decouples the algorithms from the implementations of the underlying linear algebra objects. This lets Belos exploit the latest hardware without changes to the code. Belos favors algorithms that solve higherlevel problems, such as multiple simultaneous linear systems and sequences of related linear systems, faster than standard algorithms. The package also supports extendedprecision and mixedprecision algorithms. Together, Amesos2 and Belos form a complete suite of sparse linear solvers. 1
Received...
"... Block preconditioners for finite element discretization of incompressible flow with thermal convection ..."
Abstract
 Add to MetaCart
(Show Context)
Block preconditioners for finite element discretization of incompressible flow with thermal convection
An Efficient Parallel Solution to the WignerPoisson Equations
"... A new model for studying the behavior of nanoscale tunneling devices has been developed in C++ using the WignerPoisson formulation. This model incorporates the parallel solvers of Sandia National Lab’s Trilinos software with the efficient use of parallel data structures to create a code that scales ..."
Abstract
 Add to MetaCart
(Show Context)
A new model for studying the behavior of nanoscale tunneling devices has been developed in C++ using the WignerPoisson formulation. This model incorporates the parallel solvers of Sandia National Lab’s Trilinos software with the efficient use of parallel data structures to create a code that scales well to a high number of processors. It also incorporates nonuniform meshes to discretize the solution space and higher order numerical methods to reduce simulation run times and increase numerical accuracy. The improvements inherent in the new C++ model will improve the quality of numerical simulations, and allow longer and more complex nanoscale devices to be modeled. 1.
ON THE PERFORMANCE OF THE VARIATIONAL MULTISCALE FORMULATION FOR SUBSURFACE FLOW AND TRANSPORT IN HETEROGENEOUS POROUS MEDIA
"... Abstract. The following work compares two popular mixed finite elements used to model subsurface flow and transport in heterogeneous porous media; the lowest order RaviartThomas element and the variational multiscale stabilized element. Comparison is made based on performance for several problems ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. The following work compares two popular mixed finite elements used to model subsurface flow and transport in heterogeneous porous media; the lowest order RaviartThomas element and the variational multiscale stabilized element. Comparison is made based on performance for several problems of engineering relevance that involve highly heterogenous material properties (permeability ratios of up to 1×105), open flow boundary conditions (pressure driven flows), and large scale domains in two dimensions. Numerical experiments are performed to show the degree to which mass conservation is violated when a flow field computed using either element is used as the advection velocity in a transport model. The results reveal that the variational multiscale element shows considerable mass production or loss for problems that involve flow tangential to layers of differing permeability, but marginal violation of local mass balance for problems of less orthogonality in the permeability. The results are useful in establishing rudimentary estimates of the error produced by using the variational mutliscale element for several different types of problems. 1.
DAE Tools: equationbased objectoriented modelling, simulation and optimisation software
"... In this work, DAE Tools modelling, simulation and optimisation software, its programming paradigms andmain features are presented. The current approaches to mathematical modelling such as the use of modelling languages and generalpurpose programming languages are analysed. The common set of capabil ..."
Abstract
 Add to MetaCart
In this work, DAE Tools modelling, simulation and optimisation software, its programming paradigms andmain features are presented. The current approaches to mathematical modelling such as the use of modelling languages and generalpurpose programming languages are analysed. The common set of capabilities required by the typical simulation software are discussed, and the shortcomings of the current approaches recognised. A new hybrid approach is introduced, and the modelling languages and the hybrid approach are compared in terms of the grammar, compiler, parser and interpreter requirements, maintainability and portability. The most important characteristics of the new approach are discussed, such as: (1) support for the runtime model generation; (2) support for the runtime simulation setup; (3) support for complex runtime operating procedures; (4) interoperability with the third party software packages (i.e. NumPy/SciPy); (5) suitability for embedding and use as a web application or software as a service; and (6) codegeneration, model exchange and cosimulation capabilities. The benefits of an equationbased approach to modelling, implemented in a fourth generation objectoriented general purpose programming language such as Python are discussed. The architecture and the software implementation details as well as the type of problems that can be solved using DAE Tools software are described. Finally, some applications of the software at different levels of abstraction are presented, and its embedding capabilities and suitability for use as a software as a service is demonstrated.