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Register a new userBLUES function method in computational physics
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We introduce a computational method in physics that goes beyond linear use of equation superposition (BLUES). A BLUES function is defined as a solution of a nonlinear differential equation (DE) with a delta source that is at the same time a Greens function for a related linear DE. For an arbitrary source, the BLUES function can be used to construct an exact solution to the nonlinear DE with a different, but related source. Alternatively, the BLUES function can be used to construct an approximate piecewise analytical solution to the nonlinear DE with an arbitrary source. For this alternative use the related linear DE need not be known. The method is illustrated in a few examples using analytical calculations and numerical computations. Areas for further applications are suggested.
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An iteration sequence based on the BLUES (beyond linear use of equation superposition) function method is presented for calculating analytic approximants to solutions of nonlinear partial differential equations. This extends previous work using this method for nonlinear ordinary differential equations with an external source term. Now, the initial condition plays the role of the source. The method is tested on three examples: a reaction-diffusion-convection equation, the porous medium equation with growth or decay, and the nonlinear Black-Scholes equation. A comparison is made with three other methods: the Adomian decomposition method (ADM), the variational iteration method (VIM), and the variational iteration method with Green function (GVIM). As a physical application, a deterministic differential equation is proposed for interface growth under shear, combining Burgers and Kardar- Parisi-Zhang nonlinearities. Thermal noise is neglected. This model is studied with Gaussian and space-periodic initial conditions. A detailed Fourier analysis is performed and the analytic coefficients are compared with those of ADM, VIM, GVIM, and standard perturbation theory. The BLUES method turns out to be a worthwhile alternative to the other methods. The advantages that it offers ensue from the freedom of choosing judiciously the linear part, with associated Green function, and the residual containing the nonlinear part of the differential operator at hand.
The development of a package for the management of physics data is described: its design, implementation and computational benchmarks. This package improves the data management tools originally developed for Geant4 physics models based on the EADL, EEDL and EPDL97 data libraries. The implementation exploits recent evolutions of the C++ libraries appearing in the C++0x draft, which are intended for inclusion in the next C++ ISO Standard. The new tools improve the computational performance of physics data management.
Computational physics problems often have a common set of aspects to them that any particular numerical code will have to address. Because these aspects are common to many problems, having a framework already designed and ready to use will not only speed the development of new codes, but also enhance compatibility between codes. Some of the most common aspects of computational physics problems are: a grid, a clock which tracks the flow of the simulation, and a set of models describing the dynamics of various quantities on the grid. Having a framework that could deal with these basic aspects of the simulation in a common way could provide great value to computational scientists by solving various numerical and class design issues that routinely arise. This paper describes the newly developed computational framework that we have built for rapidly prototyping new physics codes. This framework, called turboPy, is a lightweight physics modeling framework based on the design of the particle-in-cell code turboWAVE. It implements a class (called Simulation) which drives the simulation and manages communication between physics modules, a class (called PhysicsModule) which handles the details of the dynamics of the various parts of the problem, and some additional classes such as a Grid class and a Diagnostic class to handle various ancillary issues that commonly arise.
The development of a package for the management of physics data is described: its design, implementation and computational benchmarks. This package improves the data management tools originally developed for Geant4 physics models based on the EADL, EEDL and EPDL97 data libraries. The implementation exploits recent evolutions of the C++ libraries appearing in the C++0x draft, which are intended for inclusion in the next C++ ISO Standard. The new tools improve the computational performance of physics data management.
The Geant4 toolkit offers a rich variety of electromagnetic physics models; so far the evaluation of this Geant4 domain has been mostly focused on its physics functionality, while the features of its design and their impact on simulation accuracy, computational performance and facilities for verification and validation have not been the object of comparable attention yet, despite the critical role they play in many experimental applications. A new project is in progress to study the application of new design concepts and software techniques in Geant4 electromagnetic physics, and to evaluate how they can improve on the current simulation capabilities. The application of a policy-based class design is investigated as a means to achieve the objective of granular decomposition of processes; this design technique offers various advantages in terms of flexibility of configuration and computational performance. The current Geant4 physics models have been re-implemented according to the new design as a pilot project. The main features of the new design and first results of performance improvement and testing simplification are presented; they are relevant to many Geant4 applications, where computational speed and the containment of resources invested in simulation production and quality assurance play a critical role.
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