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Results for “dense LU factorization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1992

Electromagnetic scattering calculations on the Intel Touchstone Delta

During the first year's operation of the Intel Touchstone Delta system, software which solves the electric field integral equations for fields scattered from arbitrarily shaped objects has been transferred to the Delta. To fully realize the Delta's resources, an out-of-core dense matrix solution algorithm that utilizes some or all of the 90 Gbyte of concurrent file system (CFS) has been used. The largest calculation completed to date computes the fields scattered from a perfectly conducting sphere modeled by 48,672 unknown functions, resulting in a complex valued dense matrix needing 37.9 Gbyte of storage. The out-of-core LU matrix factorization algorithm was executed in 8.25 h at a rate of 10.35 Gflops. Total time to complete the calculation was 19.7 h-the additional time was used to compute the 48,672 x 48,672 matrix entries, solve the system for a given excitation, and compute observable quantities. The calculation was performed in 64-b precision.

Cwik, Tom↗
NASA NTRS1994

Parallel Preconditioning for CFD Problems on the CM-5

Up to today, preconditioning methods on massively parallel systems have faced a major difficulty. The most successful preconditioning methods in terms of accelerating the convergence of the iterative solver such as incomplete LU factorizations are notoriously difficult to implement on parallel machines for two reasons: (1) the actual computation of the preconditioner is not very floating-point intensive, but requires a large amount of unstructured communication, and (2) the application of the preconditioning matrix in the iteration phase (i.e. triangular solves) are difficult to parallelize because of the recursive nature of the computation. Here we present a new approach to preconditioning for very large, sparse, unsymmetric, linear systems, which avoids both difficulties. We explicitly compute an approximate inverse to our original matrix. This new preconditioning matrix can be applied most efficiently for iterative methods on massively parallel machines, since the preconditioning phase involves only a matrix-vector multiplication, with possibly a dense matrix. Furthermore the actual computation of the preconditioning matrix has natural parallelism. For a problem of size n, the preconditioning matrix can be computed by solving n independent small least squares problems. The algorithm and its implementation on the Connection Machine CM-5 are discussed in detail and supported by extensive timings obtained from real problem data.

Simon, Horst D.↗
NASA NTRS2014

Fifteen-Year Global Time Series of Satellite-Derived Fine Particulate Matter

Ambient fine particulate matter (PM2.5) is a leading environmental risk factor for premature mortality. We use aerosol optical depth (AOD) retrieved from two satellite instruments, MISR and SeaWiFS, to produce a unified 15-year global time series (1998−2012) of ground-level PM2.5 concentration at a resolution of 1deg x 1deg. The GEOS-Chem chemical transport model (CTM) is used to relate each individual AOD retrieval to ground-level PM2.5. Four broad areas showing significant, spatially coherent, annual trends are examined in detail: the Eastern U.S. (−0.39 +/- 0.10 micro-g/cu m/yr), the Arabian Peninsula (0.81 +/- 0.21 micro-g/cu m/yr), South Asia (0.93 +/- 0.22 micro-g/cu m/yr) and East Asia (0.79 +/- 0.27 micro-g/cu m/yr). Over the period of dense in situ observation (1999− 2012), the linear tendency for the Eastern U.S. (−0.37 +/- 0.13 micro-g/cu m/yr) agrees well with that from in situ measurements (−0.38 +/- 0.06 micro-g/cu m/yr). A GEOS-Chem simulation reveals that secondary inorganic aerosols largely explain the observed PM2.5 trend over the Eastern U.S., South Asia, and East Asia, while mineral dust largely explains the observed trend over the Arabian Peninsula.

aerosol optical depth↗