scholarly journals Parallel Multiprojection Preconditioned Methods Based on Subspace Compression

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Byron E. Moutafis ◽  
Christos K. Filelis-Papadopoulos ◽  
George A. Gravvanis
Keyword(s):  
Linear Systems ◽  
Adjacency Matrix ◽  
Sparse Linear Systems ◽  
Breadth First Search ◽  
Compression Technique ◽  
New Approach ◽  
Local Coefficient ◽  
Preconditioned Iterative ◽  
Comparative Results ◽  
Average Size

During the last decades, the continuous expansion of supercomputing infrastructures necessitates the design of scalable and robust parallel numerical methods for solving large sparse linear systems. A new approach for the additive projection parallel preconditioned iterative method based on semiaggregation and a subspace compression technique, for general sparse linear systems, is presented. The subspace compression technique utilizes a subdomain adjacency matrix and breadth first search to discover and aggregate subdomains to limit the average size of the local linear systems, resulting in reduced memory requirements. The depth of aggregation is controlled by a user defined parameter. The local coefficient matrices use the aggregates computed during the formation of the subdomain adjacency matrix in order to avoid recomputation and improve performance. Moreover, the rows and columns corresponding to the newly formed aggregates are ordered last to further reduce fill-in during the factorization of the local coefficient matrices. Furthermore, the method is based on nonoverlapping domain decomposition in conjunction with algebraic graph partitioning techniques for separating the subdomains. Finally, the applicability and implementation issues are discussed and numerical results along with comparative results are presented.

GENERIC APPROXIMATE SPARSE INVERSE MATRIX TECHNIQUES

2014 ◽  
Vol 11 (06) ◽  
pp. 1350084 ◽  
Author(s):  
CHRISTOS K. FILELIS-PAPADOPOULOS ◽  
GEORGE A. GRAVVANIS
Keyword(s):  
Linear Systems ◽  
Krylov Subspace ◽  
Coefficient Matrix ◽  
Sparse Linear Systems ◽  
Approximate Inverse ◽  
Matrix Algorithm ◽  
Sparsity Pattern ◽  
Gradient Type ◽  
Comparative Results ◽  
Conjugate Gradient Type Methods

During the last decades explicit preconditioning methods have gained interest among the scientific community, due to their efficiency for solving large sparse linear systems in conjunction with Krylov subspace iterative methods. The effectiveness of explicit preconditioning schemes relies on the fact that they are close approximants to the inverse of the coefficient matrix. Herewith, we propose a Generic Approximate Sparse Inverse (GenASPI) matrix algorithm based on ILU(0) factorization. The proposed scheme applies to matrices of any structure or sparsity pattern unlike the previous dedicated implementations. The new scheme is based on the Generic Approximate Banded Inverse (GenAbI), which is a banded approximate inverse used in conjunction with Conjugate Gradient type methods for the solution of large sparse linear systems. The proposed GenASPI matrix algorithm, is based on Approximate Inverse Sparsity patterns, derived from powers of sparsified matrices and is computed with a modified procedure based on the GenAbI algorithm. Finally, applicability and implementation issues are discussed and numerical results along with comparative results are presented.

Parallel algorithm for solving sparse linear systems

1996 ◽  
Vol 32 (19) ◽  
pp. 1766
Author(s):  
K.N. Balasubramanya Murthy ◽  
C. Siva Ram Murthy
Keyword(s):  
Parallel Algorithm ◽  
Linear Systems ◽  
Sparse Linear Systems

scholarly journals Cryogenic Exfoliation of 2D Stanene Nanosheets for Cancer Theranostics

2021 ◽  
Vol 13 (1) ◽  
Author(s):  
Jiang Ouyang ◽  
Ling Zhang ◽  
Leijiao Li ◽  
Wei Chen ◽  
Zhongmin Tang ◽  
...  
Keyword(s):  
Biomedical Applications ◽  
Density Functional ◽  
Biomedical Application ◽  
Density Functional Theory Calculations ◽  
Free Electrons ◽  
Functional Theory ◽  
New Approach ◽  
New Type ◽  
Average Size ◽  
Cancer Theranostics

Abstract Stanene (Sn)-based materials have been extensively applied in industrial production and daily life, but their potential biomedical application remains largely unexplored, which is due to the absence of the appropriate and effective methods for fabricating Sn-based biomaterials. Herein, we explored a new approach combining cryogenic exfoliation and liquid-phase exfoliation to successfully manufacture two-dimensional (2D) Sn nanosheets (SnNSs). The obtained SnNSs exhibited a typical sheet-like structure with an average size of ~ 100 nm and a thickness of ~ 5.1 nm. After PEGylation, the resulting PEGylated SnNSs (SnNSs@PEG) exhibited good stability, superior biocompatibility, and excellent photothermal performance, which could serve as robust photothermal agents for multi-modal imaging (fluorescence/photoacoustic/photothermal imaging)-guided photothermal elimination of cancer. Furthermore, we also used first-principles density functional theory calculations to investigate the photothermal mechanism of SnNSs, revealing that the free electrons in upper and lower layers of SnNSs contribute to the conversion of the photo to thermal. This work not only introduces a new approach to fabricate 2D SnNSs but also establishes the SnNSs-based nanomedicines for photonic cancer theranostics. This new type of SnNSs with great potential in the field of nanomedicines may spur a wave of developing Sn-based biological materials to benefit biomedical applications.

scholarly journals A new approach to constrained state estimation for discrete-time linear systems with unknown inputs

2017 ◽  
Vol 28 (1) ◽  
pp. 326-341 ◽  
Author(s):  
Jose Fernando Garcia Tirado ◽  
Alejandro Marquez-Ruiz ◽  
Hector Botero Castro ◽  
Fabiola Angulo
Keyword(s):  
State Estimation ◽  
Linear Systems ◽  
Discrete Time ◽  
New Approach ◽  
Unknown Inputs ◽  
Time Linear

Discretisation of sparse linear systems: An optimisation approach

2015 ◽  
Vol 80 ◽  
pp. 42-49 ◽  
Author(s):  
M. Souza ◽  
J.C. Geromel ◽  
P. Colaneri ◽  
R.N. Shorten
Keyword(s):  
Linear Systems ◽  
Sparse Linear Systems

scholarly journals Amesos2 and Belos: Direct and Iterative Solvers for Large Sparse Linear Systems

2012 ◽  
Vol 20 (3) ◽  
pp. 241-255 ◽  
Author(s):  
Eric Bavier ◽  
Mark Hoemmen ◽  
Sivasankaran Rajamanickam ◽  
Heidi Thornquist
Keyword(s):  
Linear Systems ◽  
Iterative Methods ◽  
Sparse Matrix ◽  
Sparse Matrices ◽  
Direct Methods ◽  
Iterative Solvers ◽  
Software Project ◽  
Sparse Linear Systems ◽  
Scalar Type ◽  
Mixed Precision

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 easy-to-extend C++ traits interface. It can also factor matrices whose entries have arbitrary “Scalar” type, enabling extended-precision and mixed-precision algorithms. Belos includes many different iterative methods for solving large sparse linear systems and least-squares 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 higher-level problems, such as multiple simultaneous linear systems and sequences of related linear systems, faster than standard algorithms. The package also supports extended-precision and mixed-precision algorithms. Together, Amesos2 and Belos form a complete suite of sparse linear solvers.

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