1,249 research outputs found
An iteration free backward semi-Lagrangian scheme for guiding center problems
In this paper, we develop an iteration free backward semi-Lagrangian method for nonlinear guiding center models. We apply the fourth-order central difference scheme for the Poisson equation and employ the local cubic interpolation for the spatial discretization. A key problem in the time discretization is to find the characteristic curve arriving at each grid point which is the solution of a system of highly nonlinear ODEs with a self-consistency imposed by the Poisson equation. The proposed method is based on the error correction method recently developed by the authors. For the error correction method, we introduce a modified Euler's polygon and solve the induced asymptotically linear differential equation with the midpoint quadrature rule to get the error correction term. We prove that the proposed iteration free method has convergence order at least 3 in space and 2 in time in the sense of the L2-norm. In particular, it is shown that the proposed method has a good performance in computational cost together with better conservation properties in mass, the total kinetic energy, and the enstrophy compared to the conventional second-order methods. Numerical test results are presented to support the theoretical analysis and discuss the properties of the newly proposed scheme.close0
Tools for fluid simulation control in computer graphics
Lâanimation basĂ©e sur la physique peut gĂ©nĂ©rer des systĂšmes aux comportements complexes
et réalistes. Malheureusement, contrÎler de tels systÚmes est une tùche ardue. Dans le cas
de la simulation de fluide, le processus de contrĂŽle est particuliĂšrement complexe. Bien
que de nombreuses méthodes et outils ont été mis au point pour simuler et faire le rendu
de fluides, trop peu de méthodes offrent un contrÎle efficace et intuitif sur une simulation
de fluide. Ătant donnĂ© que le coĂ»t associĂ© au contrĂŽle vient souvent sâadditionner au coĂ»t
de la simulation, appliquer un contrÎle sur une simulation à plus haute résolution rallonge
chaque itĂ©ration du processus de crĂ©ation. Afin dâaccĂ©lĂ©rer ce processus, lâĂ©dition peut se
faire sur une simulation basse résolution moins coûteuse. Nous pouvons donc considérer que
la crĂ©ation dâun fluide contrĂŽlĂ© peut se diviser en deux phases: une phase de contrĂŽle durant
laquelle un artiste modifie le comportement dâune simulation basse rĂ©solution, et une phase
dâaugmentation de dĂ©tail durant laquelle une version haute rĂ©solution de cette simulation
est gĂ©nĂ©rĂ©e. Cette thĂšse prĂ©sente deux projets, chacun contribuant Ă lâĂ©tat de lâart reliĂ© Ă
chacune de ces deux phases.
Dans un premier temps, on introduit un nouveau systÚme de contrÎle de liquide représenté
par un modĂšle particulaire. Ă lâaide de ce systĂšme, un artiste peut sĂ©lectionner dans une base
de donnĂ©es une parcelle de liquide animĂ© prĂ©calculĂ©e. Cette parcelle peut ensuite ĂȘtre placĂ©e
dans une simulation afin dâen modifier son comportement. Ă chaque pas de simulation, notre
systĂšme utilise la liste de parcelles actives afin de reproduire localement la vision de lâartiste.
Une interface graphique intuitive a été développée, inspirée par les logiciels de montage vidéo,
et permettant Ă un utilisateur non expert de simplement Ă©diter une simulation de liquide.
Dans un second temps, une mĂ©thode dâaugmentation de dĂ©tail est dĂ©crite. Nous proposons
dâajouter une Ă©tape supplĂ©mentaire de suivi aprĂšs lâĂ©tape de projection du champ de
vitesse dâune simulation de fumĂ©e eulĂ©rienne classique. Durant cette Ă©tape, un champ de
perturbations de vitesse non-divergent est calculé, résultant en une meilleure correspondance
des densitĂ©s Ă haute et Ă basse rĂ©solution. Lâanimation de fumĂ©e rĂ©sultante reproduit fidĂšlement
lâaspect grossier de la simulation dâentrĂ©e, tout en Ă©tant augmentĂ©e Ă lâaide de dĂ©tails
simulés.Physics-based animation can generate dynamic systems of very complex and realistic behaviors.
Unfortunately, controlling them is a daunting task. In particular, fluid simulation
brings up particularly difficult problems to the control process. Although many methods
and tools have been developed to convincingly simulate and render fluids, too few methods
provide efficient and intuitive control over a simulation. Since control often comes with extra
computations on top of the simulation cost, art-directing a high-resolution simulation leads
to long iterations of the creative process. In order to shorten this process, editing could be
performed on a faster, low-resolution model. Therefore, we can consider that the process of
generating an art-directed fluid could be split into two stages: a control stage during which
an artist modifies the behavior of a low-resolution simulation, and an upresolution stage
during which a final high-resolution version of this simulation is driven. This thesis presents
two projects, each one improving on the state of the art related to each of these two stages.
First, we introduce a new particle-based liquid control system. Using this system, an
artist selects patches of precomputed liquid animations from a database, and places them in
a simulation to modify its behavior. At each simulation time step, our system uses these entities
to control the simulation in order to reproduce the artistâs vision. An intuitive graphical
user interface inspired by video editing tools has been developed, allowing a nontechnical
user to simply edit a liquid animation.
Second, a tracking solution for smoke upresolution is described. We propose to add an
extra tracking step after the projection of a classical Eulerian smoke simulation. During
this step, we solve for a divergence-free velocity perturbation field resulting in a better
matching of the low-frequency density distribution between the low-resolution guide and the
high-resolution simulation. The resulting smoke animation faithfully reproduces the coarse
aspect of the low-resolution input, while being enhanced with simulated small-scale details
Some numerical aspects of the conservative PSM scheme in a 4D drift-kinetic code.
The purpose of this work is simulation of magnetised plasmas in the ITER project framework. In this context, kinetic Vlasov-Poisson like models are used to simulate core turbulence in the tokamak in a toroidal geometry. This leads to heavy simulations because a 6D dimensional problem has to be solved, even if reduced to a 5D in so called gyrokinetic models. Accurate schemes, parallel algorithms need to be designed to bear these simulations. This paper describes the numerical studies to improve robustness of the conservative PSM scheme in the context of its development in the GYSELA code. In this paper, we only consider the 4D drift-kinetic model which is the backbone of the 5D gyrokinetic models and relevant to build a robust and accurate numerical method
A Survey of Matrix Completion Methods for Recommendation Systems
In recent years, the recommendation systems have become increasingly popular and have been used in a broad variety of applications. Here, we investigate the matrix completion techniques for the recommendation systems that are based on collaborative filtering. The collaborative filtering problem can be viewed as predicting the favorability of a user with respect to new items of commodities. When a rating matrix is constructed with users as rows, items as columns, and entries as ratings, the collaborative filtering problem can then be modeled as a matrix completion problem by filling out the unknown elements in the rating matrix. This article presents a comprehensive survey of the matrix completion methods used in recommendation systems. We focus on the mathematical models for matrix completion and the corresponding computational algorithms as well as their characteristics and potential issues. Several applications other than the traditional user-item association prediction are also discussed
Seamless cross-scale modeling with SCHISM
We present a new 3D unstructured-grid model (SCHISM) which is an upgrade from an existing model (SELFE). The new advection scheme for the momentum equation includes an iterative smoother to reduce excess mass produced by higher-order kriging method, and a new viscosity formulation is shown to work robustly for generic unstructured grids and effectively filter out spurious modes without introducing excessive dissipation. A new higher-order implicit advection scheme for transport (TVD2) is proposed to effectively handle a wide range of Courant numbers as commonly found in typical cross-scale applications. The addition of quadrangular elements into the model, together with a recently proposed, highly flexible vertical grid system (Zhang et al., A new vertical coordinate system for a 3D unstructured-grid model. Ocean Model. 85, 2015), leads to model polymorphism that unifies 1D/2DH/2DV/3D cells in a single model grid. Results from several test cases demonstrate the model\u27s good performance in the eddying regime, which presents greater challenges for unstructured-grid models and represents the last missing link for our cross-scale model. The model can thus be used to simulate cross-scale processes in a seamless fashion (i.e. from deep ocean into shallow depths). Published by Elsevier Ltd
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