Yang Cheng, Bin Jia, Ming Xin

The International Conference on Computational & Experimental Engineering and Sciences, Vol.16, No.2, pp. 33-34, 2011, DOI:10.3970/icces.2011.016.033

Abstract A sparse grid approach to orbit uncertainty propagation is presented. Efficient and accurate uncertainty propagation methods for nonlinear dynamic systems have been of enormous interest to space object tracking. Recent methods include those based on the time evolution of the probability density function, the statistical moments, the random samples, or a sum of Gaussian components. The idea of the sparse grid method for orbit uncertainty propagation is to represent the initial uncertainty by a sparse grid, propagate the sparse grid points individually through the nonlinear orbit dynamics, and compute the statistical moments from the propagated sparse grid points. The Smolyak… More >

Akira Matsumoto^1,*, Taku Itoh², Soichiro Ikuno¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.21, No.2, pp. 43-43, 2019, DOI:10.32604/icces.2019.05496

Abstract In this study, an improvement technique of convergence property of Communication Avoiding (CA) Kyrlov subspace method is proposed, and parallelization efficiencies of CA Krylov subspace method is numerically investigated. As is known that most of all the procedures of the Krylov subspace method are constituted by addition of vectors, inner products and multiplication of matrices and vectors. These operations are very easy to derive a parallelization efficiency. However, the candidate coefficient matrices of linear system obtained from the numerical analysis such as Finite Element Method are large sparse matrices, and communications occur between Processing Units at short intervals in parallel… More >

Qidi Wu¹, Yibing Li¹, Yun Lin^1,*, Ruolin Zhou²

CMC-Computers, Materials & Continua, Vol.56, No.1, pp. 91-105, 2018, DOI: 10.3970/cmc.2018.02771

Abstract The conventional sparse representation-based image classification usually codes the samples independently, which will ignore the correlation information existed in the data. Hence, if we can explore the correlation information hidden in the data, the classification result will be improved significantly. To this end, in this paper, a novel weighted supervised spare coding method is proposed to address the image classification problem. The proposed method firstly explores the structural information sufficiently hidden in the data based on the low rank representation. And then, it introduced the extracted structural information to a novel weighted sparse representation model to code the samples in… More >

E-N.G. Grylonakis¹, C.K. Filelis-Papadopoulos¹, G.A. Gravvanis¹

CMES-Computer Modeling in Engineering & Sciences, Vol.109-110, No.6, pp. 505-517, 2015, DOI:10.3970/cmes.2015.109.505

Abstract A new transform method for solving boundary value problems in two dimensions was proposed by A.S. Fokas, namely the unified transform. This approach seeks a solution to the unknown boundary values by solving a global relation, using the known boundary data. This relation can be used to characterize the Dirichlet to Neumann map. For the numerical solution of the global relation, a collocation-type method was recently introduced. Hence, the considered method is used for solving the 2D Laplace equation in several irregular convex polygons. The linear system, resulting from the collocation-type method, was solved by the Explicit Preconditioned Generalized Minimum… More >

George A. Gravvanis¹, Christos K. Filelis-Papadopoulos¹, Paschalis I.Matskanidis¹

CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.4, pp. 323-345, 2014, DOI:10.3970/cmes.2014.100.323

Abstract Since the introduction of the Algebraic MultiGrid algorithm (AMG) over twenty years ago, significant progress has been made in improving the coarsening and the convergence behavior of the method. In this paper, an AMG method is introduced that utilizes a new generic approximate inverse algorithm as a smoother in conjunction with common coarsening techniques, such as classical Ruge-Stüben coarsening, CLJP and PMIS coarsening. The proposed approximate inverse scheme, namely Generic Approximate Banded Inverse (GenAbI), is a banded approximate inverse based on Incomplete LU factorization with zero fill–in (ILU(0)). The new class of Generic Approximate Banded Inverse can be computed for… More >

R.H. Haney¹, R.V. Mohan²

CMES-Computer Modeling in Engineering & Sciences, Vol.95, No.5, pp. 431-452, 2013, DOI:10.3970/cmes.2013.095.431

Abstract The use of Graphics Processing Units (GPUs) as co-processors for single CPU/GPU computing systems has become pronounced in high performance computing research, however the solution of truly large scale computationally intensive problems require the utilization of multiple computing nodes. Multiple CPU/GPU computing systems bring new complexities to the observed performance of computationally intensive applications, the more salient of which is the cost of local CPU-GPU host and intra-nodal communication. This paper compares and analyzes the performance of a computationally intensive application represented by resin infusion flow during liquid composite molding process for the manufacture of structural composites application via two… More >

G.A. Gravvanis¹, K.M. Giannoutakis¹

CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.2, pp. 69-82, 2006, DOI:10.3970/cmes.2006.016.069

Abstract A new class of normalized explicit optimized approximate inverse finite element matrix techniques, based on normalized finite element approximate factorization procedures, for solving sparse linear systems resulting from the finite element discretization of partial differential equations in three space variables are introduced. A new parallel normalized explicit preconditioned conjugate gradient square method in conjunction with normalized approximate inverse finite element matrix techniques for solving efficiently sparse finite element linear systems on distributed memory systems is also presented along with theoretical estimates on speedups and efficiency. The performance on a distributed memory machine, using Message Passing Interface (MPI) communication library, is… More >

Gerhard Klimeck^1,2, Fabiano Oyafuso², Timothy B. Boykin³, R. Chris Bowen², Paul von Allmen⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.5, pp. 601-642, 2002, DOI:10.3970/cmes.2002.003.601

Abstract Material layers with a thickness of a few nanometers are common-place in today's semiconductor devices. Before long, device fabrication methods will reach a point at which the other two device dimensions are scaled down to few tens of nanometers. The total atom count in such deca-nano devices is reduced to a few million. Only a small finite number of "free'' electrons will operate such nano-scale devices due to quantized electron energies and electron charge. This work demonstrates that the simulation of electronic structure and electron transport on these length scales must not only be fundamentally quantum mechanical, but it must… More >

G.A. Gravvanis¹, K.M. Giannoutakis²

CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.4, pp. 305-330, 2011, DOI:10.3970/cmes.2011.071.305

Abstract In this paper we present parallel explicit approximate inverse matrix techniques for solving sparse linear systems on shared memory systems, which are derived using the finite element method for biharmonic equations in three space variables. Our approach for solving such equations is by considering the biharmonic equation as a coupled equation approach (pair of Poisson equation), using a FE approximation scheme, yielding an inner-outer iteration method. Additionally, parallel approximate inverse matrix algorithms are introduced for the efficient solution of sparse linear systems, based on an anti-diagonal computational approach that eliminates the data dependencies. Parallel explicit preconditioned conjugate gradient-type schemes in… More >

G.A. Gravvanis, K.M. Giannoutakis¹

CMES-Computer Modeling in Engineering & Sciences, Vol.32, No.1, pp. 35-44, 2008, DOI:10.3970/cmes.2008.032.035

Abstract A new parallel normalized optimized approximate inverse algorithm, based on the concept of the ``fish bone'' computational approach with cyclic distribution of the processors satisfying an antidiagonal data dependency, for computing classes of explicit approximate inverses, is introduced for symmetric multiprocessor systems. The parallel normalized explicit approximate inverses are used in conjunction with parallel normalized explicit preconditioned conjugate gradient square schemes, for the efficient solution of finite element sparse linear systems. The parallel design and implementation issues of the new proposed algorithms are discussed and the parallel performance is presented, using OpenMP. More >