32 research outputs found
Adaptation and Evaluation of the Multisplitting-Newton and Waveform Relaxation Methods Over Distributed Volatile Environments
International audienceThis paper presents new adaptations of two methods that solve large differential equations systems, to the grid context. The first method isbased on the Multisplitting concept and the second on the Waveform Relaxation concept. Their adaptations are implemented according to the asynchronous iteration model which is well suited to volatile architectures that suffer from high latency networks. Many experiments were conducted to evaluate and compare the accuracy and performance of both methods while solving the advection-diffusion problem over heterogeneous, distributed and volatile architectures. The JACEP2P-V2 middleware provided the fault tolerant asynchronous environment, required for these experiments
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Implicit solution of large-scale radiation - material energy transfer problems
Modeling of radiation-diffusion processes has traditionally been accomplished through simulations based on decoupling and linearizing the basic physics equations. By applying these techniques, physicists have simplified their model enough that problems of moderate sizes could be solved. However, new applications demand the simulation of larger problems for which the inaccuracies and nonscalability of current algorithms prevent solution. Recent work in iterative methods has provided computational scientists with new tools for solving these problems. In this paper, we present an algorithm for the implicit solution of the multi- group diffusion approximation coupled to an electron temperature equation. This algorithm uses a stiff ODE solver coupled with Newton's method for solving the implicit equations arising at each time step. The Jacobian systems are solved by applying GMRES preconditioned with a semicoarsening multigrid algorithm. By combining the nonlinear Newton iteration with a multigrid preconditioner, we take advantage of the fast, robust nonlinear convergence of Newton's method and the scalability of the linear multigrid method. Numerical results show that the method is accurate and scalable
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User documentation for KINSOL, a nonlinear solver for sequential and parallel computers
KINSOL is a general purpose nonlinear system solver callable from either C or Fortran programs It is based on NKSOL [3], but is written in ANSI-standard C rather than Fortran77 Its most notable feature is that it uses Krylov Inexact Newton techniques in the system`s approximate solution, thus sharing significant modules previously written within CASC at LLNL to support CVODE[6, 7]/PVODE[9, 5] It also requires almost no matrix storage for solving the Newton equations as compared to direct methods The name KINSOL is derived from those techniques Krylov Inexact Newton SOLver The package was arranged so that selecting one of two forms of a single module in the compilation process will allow the entire package to be created in either sequential (serial) or parallel form The parallel version of KINSOL uses MPI (Message-Passing Interface) [8] and an appropriately revised version of the vector module NVECTOR, as mentioned above, to achieve parallelism and portability KINSOL in parallel form is intended for the SPMD (Single Program Multiple Data) model with distributed memory, in which all vectors are identically distributed across processors In particular, the vector module NVECTOR is designed to help the user assign a contiguous segment of a given vector to each of the processors for parallel computation Several primitives were added to NVECTOR as originally written for PVODE to implement KINSOL KINSOL has been run on a Cray-T3D, an eight- processor DEC ALPHA and a cluster of workstations It is currently being used in a simulation of tokamak edge plasmas and in groundwater two-phase flow studies at LLNL The remainder of this paper is organized as follows Section 2 sets the mathematical notation and summarizes the basic methods Section 3 summarizes the organization of the KINSOL solver, while Section 4 summarizes its usage Section 5 describes a preconditioner module, Section 6 describes a set of Fortran/C interfaces, Section 7 describes an example problem, and Section 8 discusses availabilit
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SciCADE 95: International conference on scientific computation and differential equations
This report consists of abstracts from the conference. Topics include algorithms, computer codes, and numerical solutions for differential equations. Linear and nonlinear as well as boundary-value and initial-value problems are covered. Various applications of these problems are also included