124 research outputs found
Computable Finite Element Error Bounds for Poisson's Equation
New explicit finite element error bounds are presented for approximation by (1) piecewise linear elements over triangles and (2) piecewise bilinear elements over squares and rectangles. By this the error bounds given in Bamhill, Brown & Mitchell (1981) are improve
Perfectly Matched Layers in a Divergence Preserving ADI Scheme for Electromagnetics
For numerical simulations of highly relativistic and transversely accelerated
charged particles including radiation fast algorithms are needed. While the
radiation in particle accelerators has wavelengths in the order of 100 um the
computational domain has dimensions roughly 5 orders of magnitude larger
resulting in very large mesh sizes. The particles are confined to a small area
of this domain only. To resolve the smallest scales close to the particles
subgrids are envisioned. For reasons of stability the alternating direction
implicit (ADI) scheme by D. N. Smithe et al. (J. Comput. Phys. 228 (2009)
pp.7289-7299) for Maxwell equations has been adopted. At the boundary of the
domain absorbing boundary conditions have to be employed to prevent reflection
of the radiation. In this paper we show how the divergence preserving ADI
scheme has to be formulated in perfectly matched layers (PML) and compare the
performance in several scenarios.Comment: 8 pages, 6 figure
A Parallel General Purpose Multi-Objective Optimization Framework, with Application to Beam Dynamics
Particle accelerators are invaluable tools for research in the basic and
applied sciences, in fields such as materials science, chemistry, the
biosciences, particle physics, nuclear physics and medicine. The design,
commissioning, and operation of accelerator facilities is a non-trivial task,
due to the large number of control parameters and the complex interplay of
several conflicting design goals. We propose to tackle this problem by means of
multi-objective optimization algorithms which also facilitate a parallel
deployment. In order to compute solutions in a meaningful time frame a fast and
scalable software framework is required. In this paper, we present the
implementation of such a general-purpose framework for simulation-based
multi-objective optimization methods that allows the automatic investigation of
optimal sets of machine parameters. The implementation is based on a
master/slave paradigm, employing several masters that govern a set of slaves
executing simulations and performing optimization tasks. Using evolutionary
algorithms as the optimizer and OPAL as the forward solver, validation
experiments and results of multi-objective optimization problems in the domain
of beam dynamics are presented. The high charge beam line at the Argonne
Wakefield Accelerator Facility was used as the beam dynamics model. The 3D beam
size, transverse momentum, and energy spread were optimized
Piecewise Linear Approximation of Empirical Distributions under a Wasserstein Distance Constraint
A Fast Parallel Poisson Solver on Irregular Domains Applied to Beam Dynamic Simulations
We discuss the scalable parallel solution of the Poisson equation within a
Particle-In-Cell (PIC) code for the simulation of electron beams in particle
accelerators of irregular shape. The problem is discretized by Finite
Differences. Depending on the treatment of the Dirichlet boundary the resulting
system of equations is symmetric or `mildly' nonsymmetric positive definite. In
all cases, the system is solved by the preconditioned conjugate gradient
algorithm with smoothed aggregation (SA) based algebraic multigrid (AMG)
preconditioning. We investigate variants of the implementation of SA-AMG that
lead to considerable improvements in the execution times. We demonstrate good
scalability of the solver on distributed memory parallel processor with up to
2048 processors. We also compare our SAAMG-PCG solver with an FFT-based solver
that is more commonly used for applications in beam dynamics
An Alternative Parameterization of R-matrix Theory
An alternative parameterization of R-matrix theory is presented which is
mathematically equivalent to the standard approach, but possesses features
which simplify the fitting of experimental data. In particular there are no
level shifts and no boundary-condition constants which allows the positions and
partial widths of an arbitrary number levels to be easily fixed in an analysis.
These alternative parameters can be converted to standard R-matrix parameters
by a straightforward matrix diagonalization procedure. In addition it is
possible to express the collision matrix directly in terms of the alternative
parameters.Comment: 8 pages; accepted for publication in Phys. Rev. C; expanded Sec. IV,
added Sec. VI, added Appendix, corrected typo
Computationally-Optimized Bone Mechanical Modeling from High-Resolution Structural Images
Image-based mechanical modeling of the complex micro-structure of human bone has shown promise as a non-invasive method for characterizing bone strength and fracture risk in vivo. In particular, elastic moduli obtained from image-derived micro-finite element (μFE) simulations have been shown to correlate well with results obtained by mechanical testing of cadaveric bone. However, most existing large-scale finite-element simulation programs require significant computing resources, which hamper their use in common laboratory and clinical environments. In this work, we theoretically derive and computationally evaluate the resources needed to perform such simulations (in terms of computer memory and computation time), which are dependent on the number of finite elements in the image-derived bone model. A detailed description of our approach is provided, which is specifically optimized for μFE modeling of the complex three-dimensional architecture of trabecular bone. Our implementation includes domain decomposition for parallel computing, a novel stopping criterion, and a system for speeding up convergence by pre-iterating on coarser grids. The performance of the system is demonstrated on a dual quad-core Xeon 3.16 GHz CPUs equipped with 40 GB of RAM. Models of distal tibia derived from 3D in-vivo MR images in a patient comprising 200,000 elements required less than 30 seconds to converge (and 40 MB RAM). To illustrate the system's potential for large-scale μFE simulations, axial stiffness was estimated from high-resolution micro-CT images of a voxel array of 90 million elements comprising the human proximal femur in seven hours CPU time. In conclusion, the system described should enable image-based finite-element bone simulations in practical computation times on high-end desktop computers with applications to laboratory studies and clinical imaging
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