4,592 research outputs found
Multigrid waveform relaxation for the time-fractional heat equation
In this work, we propose an efficient and robust multigrid method for solving
the time-fractional heat equation. Due to the nonlocal property of fractional
differential operators, numerical methods usually generate systems of equations
for which the coefficient matrix is dense. Therefore, the design of efficient
solvers for the numerical simulation of these problems is a difficult task. We
develop a parallel-in-time multigrid algorithm based on the waveform relaxation
approach, whose application to time-fractional problems seems very natural due
to the fact that the fractional derivative at each spatial point depends on the
values of the function at this point at all earlier times. Exploiting the
Toeplitz-like structure of the coefficient matrix, the proposed multigrid
waveform relaxation method has a computational cost of
operations, where is the number of time steps and is the number of
spatial grid points. A semi-algebraic mode analysis is also developed to
theoretically confirm the good results obtained. Several numerical experiments,
including examples with non-smooth solutions and a nonlinear problem with
applications in porous media, are presented
Three real-space discretization techniques in electronic structure calculations
A characteristic feature of the state-of-the-art of real-space methods in
electronic structure calculations is the diversity of the techniques used in
the discretization of the relevant partial differential equations. In this
context, the main approaches include finite-difference methods, various types
of finite-elements and wavelets. This paper reports on the results of several
code development projects that approach problems related to the electronic
structure using these three different discretization methods. We review the
ideas behind these methods, give examples of their applications, and discuss
their similarities and differences.Comment: 39 pages, 10 figures, accepted to a special issue of "physica status
solidi (b) - basic solid state physics" devoted to the CECAM workshop "State
of the art developments and perspectives of real-space electronic structure
techniques in condensed matter and molecular physics". v2: Minor stylistic
and typographical changes, partly inspired by referee comment
Simulating Radiating and Magnetized Flows in Multi-Dimensions with ZEUS-MP
This paper describes ZEUS-MP, a multi-physics, massively parallel, message-
passing implementation of the ZEUS code. ZEUS-MP differs significantly from the
ZEUS-2D code, the ZEUS-3D code, and an early "version 1" of ZEUS-MP distributed
publicly in 1999. ZEUS-MP offers an MHD algorithm better suited for
multidimensional flows than the ZEUS-2D module by virtue of modifications to
the Method of Characteristics scheme first suggested by Hawley and Stone
(1995), and is shown to compare quite favorably to the TVD scheme described by
Ryu et. al (1998). ZEUS-MP is the first publicly-available ZEUS code to allow
the advection of multiple chemical (or nuclear) species. Radiation hydrodynamic
simulations are enabled via an implicit flux-limited radiation diffusion (FLD)
module. The hydrodynamic, MHD, and FLD modules may be used in one, two, or
three space dimensions. Self gravity may be included either through the
assumption of a GM/r potential or a solution of Poisson's equation using one of
three linear solver packages (conjugate-gradient, multigrid, and FFT) provided
for that purpose. Point-mass potentials are also supported. Because ZEUS-MP is
designed for simulations on parallel computing platforms, considerable
attention is paid to the parallel performance characteristics of each module.
Strong-scaling tests involving pure hydrodynamics (with and without
self-gravity), MHD, and RHD are performed in which large problems (256^3 zones)
are distributed among as many as 1024 processors of an IBM SP3. Parallel
efficiency is a strong function of the amount of communication required between
processors in a given algorithm, but all modules are shown to scale well on up
to 1024 processors for the chosen fixed problem size.Comment: Accepted for publication in the ApJ Supplement. 42 pages with 29
inlined figures; uses emulateapj.sty. Discussions in sections 2 - 4 improved
per referee comments; several figures modified to illustrate grid resolution.
ZEUS-MP source code and documentation available from the Laboratory for
Computational Astrophysics at http://lca.ucsd.edu/codes/currentcodes/zeusmp2
A general multiblock Euler code for propulsion integration. Volume 1: Theory document
A general multiblock Euler solver was developed for the analysis of flow fields over geometrically complex configurations either in free air or in a wind tunnel. In this approach, the external space around a complex configuration was divided into a number of topologically simple blocks, so that surface-fitted grids and an efficient flow solution algorithm could be easily applied in each block. The computational grid in each block is generated using a combination of algebraic and elliptic methods. A grid generation/flow solver interface program was developed to facilitate the establishment of block-to-block relations and the boundary conditions for each block. The flow solver utilizes a finite volume formulation and an explicit time stepping scheme to solve the Euler equations. A multiblock version of the multigrid method was developed to accelerate the convergence of the calculations. The generality of the method was demonstrated through the analysis of two complex configurations at various flow conditions. Results were compared to available test data. Two accompanying volumes, user manuals for the preparation of multi-block grids (vol. 2) and for the Euler flow solver (vol. 3), provide information on input data format and program execution
Study of second order upwind differencing in a recirculating flow
The accuracy and stability of the second order upwind differencing scheme was investigated. The solution algorithm employed is based on a coupled solution of the nonlinear finite difference equations by the multigrid technique. Calculations have been made of the driven cavity flow for several Reynolds numbers and finite difference grids. In comparison with the hybrid differencing, the second order upwind differencing is somewhat more accurate but it is not monotonically accurate with mesh refinement. Also, the convergence of the solution algorithm deteriorates with the use of the second order upwind differencing
A bibliography on parallel and vector numerical algorithms
This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also
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