99,638 research outputs found
ADER-WENO Finite Volume Schemes with Space-Time Adaptive Mesh Refinement
We present the first high order one-step ADER-WENO finite volume scheme with
Adaptive Mesh Refinement (AMR) in multiple space dimensions. High order spatial
accuracy is obtained through a WENO reconstruction, while a high order one-step
time discretization is achieved using a local space-time discontinuous Galerkin
predictor method. Due to the one-step nature of the underlying scheme, the
resulting algorithm is particularly well suited for an AMR strategy on
space-time adaptive meshes, i.e.with time-accurate local time stepping. The AMR
property has been implemented 'cell-by-cell', with a standard tree-type
algorithm, while the scheme has been parallelized via the Message Passing
Interface (MPI) paradigm. The new scheme has been tested over a wide range of
examples for nonlinear systems of hyperbolic conservation laws, including the
classical Euler equations of compressible gas dynamics and the equations of
magnetohydrodynamics (MHD). High order in space and time have been confirmed
via a numerical convergence study and a detailed analysis of the computational
speed-up with respect to highly refined uniform meshes is also presented. We
also show test problems where the presented high order AMR scheme behaves
clearly better than traditional second order AMR methods. The proposed scheme
that combines for the first time high order ADER methods with space--time
adaptive grids in two and three space dimensions is likely to become a useful
tool in several fields of computational physics, applied mathematics and
mechanics.Comment: With updated bibliography informatio
Spectral Volume Method: application to Euler equations and performance appraisal
The compact high-order "Spectral Volume Method" designed for conservation laws on unstructured grids is presented. Its spectral reconstruction is exposed briefly and its applications to the Euler equations are presented through several test cases to assess its accuracy and stability. Comparisons with usual methods such as MUSCL show the superiority of SVM. The SVM method arises as a high-order accurate scheme, geometrically flexible and computationally efficient
Assessment of the Spectral Volume Method on inviscid and viscous flows
The compact high-order "Spectral Volume Method" designed for conservation laws on unstructured grids is presented. Its spectral reconstruction is exposed briefly and its applications to the Euler equations are presented through several test cases to assess its accuracy and stability. Comparisons with classical methods such as MUSCL show the superiority of SVM. The SVM method arises as a high-order accurate scheme, geometrically flexible and computationally efficient
Beam Orientation Optimization for Intensity Modulated Radiation Therapy using Adaptive l1 Minimization
Beam orientation optimization (BOO) is a key component in the process of IMRT
treatment planning. It determines to what degree one can achieve a good
treatment plan quality in the subsequent plan optimization process. In this
paper, we have developed a BOO algorithm via adaptive l_1 minimization.
Specifically, we introduce a sparsity energy function term into our model which
contains weighting factors for each beam angle adaptively adjusted during the
optimization process. Such an energy term favors small number of beam angles.
By optimizing a total energy function containing a dosimetric term and the
sparsity term, we are able to identify the unimportant beam angles and
gradually remove them without largely sacrificing the dosimetric objective. In
one typical prostate case, the convergence property of our algorithm, as well
as the how the beam angles are selected during the optimization process, is
demonstrated. Fluence map optimization (FMO) is then performed based on the
optimized beam angles. The resulted plan quality is presented and found to be
better than that obtained from unoptimized (equiangular) beam orientations. We
have further systematically validated our algorithm in the contexts of 5-9
coplanar beams for 5 prostate cases and 1 head and neck case. For each case,
the final FMO objective function value is used to compare the optimized beam
orientations and the equiangular ones. It is found that, our BOO algorithm can
lead to beam configurations which attain lower FMO objective function values
than corresponding equiangular cases, indicating the effectiveness of our BOO
algorithm.Comment: 19 pages, 2 tables, and 5 figure
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