اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOptimized Schwarz waveform relaxation for Primitive Equations of the ocean
404
0
0.0
(
0
)
تأليف
Emmanuel Audusse
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this article we are interested in the derivation of efficient domain decomposition methods for the viscous primitive equations of the ocean. We consider the rotating 3d incompressible hydrostatic Navier-Stokes equations with free surface. Performing an asymptotic analysis of the system with respect to the Rossby number, we compute an approximated Dirichlet to Neumann operator and build an optimized Schwarz waveform relaxation algorithm. We establish the well-posedness of this algorithm and present some numerical results to illustrate the method.
قيم البحث
اقرأ أيضاً
Waveform Relaxation method (WR) is a beautiful algorithm to solve Ordinary Differential Equations (ODEs). However, because of its poor convergence capability, it was rarely used. In this paper, we propose a new distributed algorithm, named Waveform T
ransmission Method (WTM), by virtually inserting waveform transmission lines into the dynamical system to achieve distributed computing of extremely large ODEs. WTM has better convergence capability than the traditional WR algorithms.
Stochastic equations play an important role in computational science, due to their ability to treat a wide variety of complex statistical problems. However, current algorithms are strongly limited by their sampling variance, which scales proportionat
e to 1/N_S for N_S samples. In this paper, we obtain a new class of variance reduction methods for treating stochastic equations, called parallel optimized sampling. The objective of parallel optimized sampling is to reduce the sampling variance in the observables of an ensemble of stochastic trajectories. This is achieved through calculating a finite set of observables - typically statistical moments - in parallel, and minimizing the errors compared to known values. The algorithm is both numerically efficient and unbiased. Importantly, it does not increase the errors in higher order moments, and generally reduces such errors as well. The same procedure is applied both to initial ensembles and to changes in a finite time-step. Results of these methods show that errors in initially optimized moments can be reduced to the machine precision level, typically around 10^(-16) in current hardware. For nonlinear stochastic equations, sampled moment errors during time-evolution are larger than this, due to error propagation effects. Even so, we provide evidence for error reductions of up to two orders of magnitude in a nonlinear equation example, for low order moments, which is a large practical benefit. The sampling variance typically scales as 1/N_S, but with the advantage of a very much smaller prefactor than for standard, non-optimized methods.
A new set of nonlocal boundary conditions are proposed for the higher modes of the 3D inviscid primitive equations. Numerical schemes using the splitting-up method are proposed for these modes. Numerical simulations of the full nonlinear primitive eq
uations are performed on a nested set of domains, and the results are discussed.
In this article, we analyse the convergence behaviour and scalability properties of the one-level Parallel Schwarz method (PSM) for domain decomposition problems in which the boundaries of many subdomains lie in the interior of the global domain. Suc
h problems arise, for instance, in solvation models in computational chemistry. Existing results on the scalability of the one-level PSM are limited to situations where each subdomain has access to the external boundary, and at most only two subdomains have a common overlap. We develop a systematic framework that allows us to bound the norm of the Schwarz iteration operator for domain decomposition problems in which subdomains may be completely embedded in the interior of the global domain and an arbitrary number of subdomains may have a common overlap.
When the obstacle problem of clamped Kirchhoff plates is discretized by a partition of unity method, the resulting discrete variational inequalities can be solved by a primal-dual active set algorithm. In this paper we develop and analyze additive Sc
hwarz preconditioners for the systems that appear in each iteration of the primal-dual active set algorithm. Numerical results that corroborate the theoretical estimates are also presented.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
