759 research outputs found
A Parallel Iterative Method for Computing Molecular Absorption Spectra
We describe a fast parallel iterative method for computing molecular
absorption spectra within TDDFT linear response and using the LCAO method. We
use a local basis of "dominant products" to parametrize the space of orbital
products that occur in the LCAO approach. In this basis, the dynamical
polarizability is computed iteratively within an appropriate Krylov subspace.
The iterative procedure uses a a matrix-free GMRES method to determine the
(interacting) density response. The resulting code is about one order of
magnitude faster than our previous full-matrix method. This acceleration makes
the speed of our TDDFT code comparable with codes based on Casida's equation.
The implementation of our method uses hybrid MPI and OpenMP parallelization in
which load balancing and memory access are optimized. To validate our approach
and to establish benchmarks, we compute spectra of large molecules on various
types of parallel machines.
The methods developed here are fairly general and we believe they will find
useful applications in molecular physics/chemistry, even for problems that are
beyond TDDFT, such as organic semiconductors, particularly in photovoltaics.Comment: 20 pages, 17 figures, 3 table
A comparative study on different parallel solvers for nonlinear analysis of complex structures
The parallelization of 2D/3D software SAPTIS is discussed for nonlinear analysis of complex structures. A comparative study is made on different parallel solvers. The numerical models are presented, including hydration models, water cooling models, modulus models, creep model, and autogenous deformation models. A finite element simulation is made for the whole process of excavation and pouring of dams using these models. The numerical results show a good agreement with the measured ones. To achieve a better computing efficiency, four parallel solvers utilizing parallelization techniques are employed: (1) a parallel preconditioned conjugate gradient (PCG) solver based on OpenMP, (2) a parallel preconditioned Krylov subspace solver based on MPI, (3) a parallel sparse equation solver based on OpenMP, and (4) a parallel GPU equation solver. The parallel solvers run either in a shared memory environment OpenMP or in a distributed memory environment MPI. A comparative study on these parallel solvers is made, and the results show that the parallelization makes SAPTIS more efficient, powerful, and adaptable
Globally stable, highly parallelizable fast transient circuit simulation via faber series
Time-domain circuit simulation based on matrix exponential has attracted renewed interested, owing to its explicit nature and global stability that enable millionth-order circuit simulation. The matrix exponential is commonly computed by Krylov subspace methods, which become inefficient when the circuit is stiff, namely, when the time constants of the circuit differ by several orders. In this paper, we utilize the truncated Faber Series for accurate evaluation of the matrix exponential even under a highly stiff system matrix arising from practical circuits. Experiments have shown that the proposed approach is globally stable, highly accurate and parallelizable, and avoids excessive memory storage demanded by Krylov subspace methods. © 2012 IEEE.published_or_final_versio
ParaExp using Leapfrog as Integrator for High-Frequency Electromagnetic Simulations
Recently, ParaExp was proposed for the time integration of linear hyperbolic
problems. It splits the time interval of interest into sub-intervals and
computes the solution on each sub-interval in parallel. The overall solution is
decomposed into a particular solution defined on each sub-interval with zero
initial conditions and a homogeneous solution propagated by the matrix
exponential applied to the initial conditions. The efficiency of the method
depends on fast approximations of this matrix exponential based on recent
results from numerical linear algebra. This paper deals with the application of
ParaExp in combination with Leapfrog to electromagnetic wave problems in
time-domain. Numerical tests are carried out for a simple toy problem and a
realistic spiral inductor model discretized by the Finite Integration
Technique.Comment: Corrected typos. arXiv admin note: text overlap with arXiv:1607.0036
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