50,984 research outputs found
Kinetic Solvers with Adaptive Mesh in Phase Space
An Adaptive Mesh in Phase Space (AMPS) methodology has been developed for
solving multi-dimensional kinetic equations by the discrete velocity method. A
Cartesian mesh for both configuration (r) and velocity (v) spaces is produced
using a tree of trees data structure. The mesh in r-space is automatically
generated around embedded boundaries and dynamically adapted to local solution
properties. The mesh in v-space is created on-the-fly for each cell in r-space.
Mappings between neighboring v-space trees implemented for the advection
operator in configuration space. We have developed new algorithms for solving
the full Boltzmann and linear Boltzmann equations with AMPS. Several recent
innovations were used to calculate the discrete Boltzmann collision integral
with dynamically adaptive mesh in velocity space: importance sampling,
multi-point projection method, and the variance reduction method. We have
developed an efficient algorithm for calculating the linear Boltzmann collision
integral for elastic and inelastic collisions in a Lorentz gas. New AMPS
technique has been demonstrated for simulations of hypersonic rarefied gas
flows, ion and electron kinetics in weakly ionized plasma, radiation and light
particle transport through thin films, and electron streaming in
semiconductors. We have shown that AMPS allows minimizing the number of cells
in phase space to reduce computational cost and memory usage for solving
challenging kinetic problems
Task-based adaptive multiresolution for time-space multi-scale reaction-diffusion systems on multi-core architectures
A new solver featuring time-space adaptation and error control has been
recently introduced to tackle the numerical solution of stiff
reaction-diffusion systems. Based on operator splitting, finite volume adaptive
multiresolution and high order time integrators with specific stability
properties for each operator, this strategy yields high computational
efficiency for large multidimensional computations on standard architectures
such as powerful workstations. However, the data structure of the original
implementation, based on trees of pointers, provides limited opportunities for
efficiency enhancements, while posing serious challenges in terms of parallel
programming and load balancing. The present contribution proposes a new
implementation of the whole set of numerical methods including Radau5 and
ROCK4, relying on a fully different data structure together with the use of a
specific library, TBB, for shared-memory, task-based parallelism with
work-stealing. The performance of our implementation is assessed in a series of
test-cases of increasing difficulty in two and three dimensions on multi-core
and many-core architectures, demonstrating high scalability
A finite-element toolbox for the stationary Gross-Pitaevskii equation with rotation
We present a new numerical system using classical finite elements with mesh
adaptivity for computing stationary solutions of the Gross-Pitaevskii equation.
The programs are written as a toolbox for FreeFem++ (www.freefem.org), a free
finite-element software available for all existing operating systems. This
offers the advantage to hide all technical issues related to the implementation
of the finite element method, allowing to easily implement various numerical
algorithms.Two robust and optimised numerical methods were implemented to
minimize the Gross-Pitaevskii energy: a steepest descent method based on
Sobolev gradients and a minimization algorithm based on the state-of-the-art
optimization library Ipopt. For both methods, mesh adaptivity strategies are
implemented to reduce the computational time and increase the local spatial
accuracy when vortices are present. Different run cases are made available for
2D and 3D configurations of Bose-Einstein condensates in rotation. An optional
graphical user interface is also provided, allowing to easily run predefined
cases or with user-defined parameter files. We also provide several
post-processing tools (like the identification of quantized vortices) that
could help in extracting physical features from the simulations. The toolbox is
extremely versatile and can be easily adapted to deal with different physical
models
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