This proceedings volume collects review articles that summarize research conducted at the Munich Centre of Advanced Computing (MAC) from 2008 to 2012. The articles address the increasing gap between what should be pos...
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ISBN:
(数字)9783642387623
ISBN:
(纸本)9783642387616;9783642387623
This proceedings volume collects review articles that summarize research conducted at the Munich Centre of Advanced Computing (MAC) from 2008 to 2012. The articles address the increasing gap between what should be possible in computationalscience and engineering due to recent advances in algorithms, hardware, and networks, and what can actually be achieved in practice; they also examinenovel computing architectures, where computation itself is a multifaceted process, with hardware awareness or ubiquitous parallelism due to many-core systems being just two of the challenges faced. Topics cover both the methodological aspects of advanced computing (algorithms, parallel computing, data exploration, software engineering) and cutting-edge applications from the fields of chemistry, the geosciences, civil and mechanical engineering, etc., reflecting the highly interdisciplinary nature of the Munich Centre of Advanced Computing.
We suggest a method for the integration of highly oscillatory systems with a single high frequency. The new method may be seen as a purely numerical way of implementing the analytical technique of stroboscopic averagi...
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ISBN:
(纸本)9783642219429
We suggest a method for the integration of highly oscillatory systems with a single high frequency. The new method may be seen as a purely numerical way of implementing the analytical technique of stroboscopic averaging. The technique may be easily implemented in combination with standard software and may be applied with variable step sizes. Numerical experiments show that the suggested algorithms may be substantially more efficient than standard numerical integrators.
This work presents a review of recent tools for multiscale simulations of liquids, ranging from simple Newtonian fluids to polymer melts. Particular attention is given to the problem of imposing the desired macro stat...
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ISBN:
(纸本)9783642219429
This work presents a review of recent tools for multiscale simulations of liquids, ranging from simple Newtonian fluids to polymer melts. Particular attention is given to the problem of imposing the desired macro state into open microscopic systems, allowing for mass, momentum and energy exchanges with the environmental state, usually provided by a continuum fluid dynamics (CFD) solver. This review intends to highlight that most of the different methods developed so far in the literature can be joined together in a general tool, which I call OPEN MD. The development of OPEN MD should be seen as an ongoing research program. A link between the micro and macro methods is the imposition of the external conditions prescribed by the macro-solver at or across the boundaries of a microscopic domain. The common methodology is the use of external particle forces within the so called particle buffer. Under this frame, OPEN MD requires minor modifications to perform state-coupling (i.e. imposing velocity and/or temperature) or flux exchange, or even any clever combination of both. This tool can be used either in molecular or mesoscopic-based research or in CFD based problems, which focus on mean flow effects arising from the underlying molecular nature. In this latter case an important goal is to allow for a general description of Non-Newtonian liquids, involving not only transfer of momentum in incompressible situations, but also mass and energy transfers between the micro and macro models.
A new coupling term for blending particle and continuum models with the Arlequin framework is investigated in this work. The coupling term is based on an integral operator defined on the overlap region that matches th...
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ISBN:
(纸本)9783642219429
A new coupling term for blending particle and continuum models with the Arlequin framework is investigated in this work. The coupling term is based on an integral operator defined on the overlap region that matches the continuum and particle solutions in an average sense. The present exposition is essentially the continuation of a previous work (Bauman et al., On the application of the Arlequin method to the coupling of particle and continuum models, computational Mechanics, 42, 511-530, 2008) in which coupling was performed in terms of an H-1-type norm. In that case, it was shown that the solution of the coupled problem was mesh-dependent or, said in another way, that the solution of the continuous coupled problem was not the intended solution. This new formulation is now consistent with the problem of interest and is virtually mesh-independent when considering a particle model consisting of a distribution of heterogeneous bonds. The mathematical properties of the formulation are studied for a one-dimensional model of harmonic springs, with varying stiffness parameters, coupled with a linear elastic bar, whose modulus is determined by classical homogenization. Numerical examples are presented for one-dimensional and two-dimensional model problems that illustrate the approximation properties of the new coupling term and the effect of mesh size.
Multiscale wave propagation problems are computationally costly to solve by traditional techniques because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have...
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ISBN:
(纸本)9783642219429
Multiscale wave propagation problems are computationally costly to solve by traditional techniques because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and analyzed new numerical methods for multiscale wave propagation in the framework of the heterogeneous multiscale method (HMM). The numerical methods couple simulations on macro- and microscales for problems with rapidly oscillating coefficients. The complexity of the new method is significantly lower than that of traditional techniques with a computational cost that is essentially independent of the smallest scale, when computing solutions at a fixed time and accuracy. We show numerical examples of the HMM applied to long time integration of wave propagation problems in both periodic and non-periodic medium. In both cases our HMM accurately captures the dispersive effects that occur. We also give a stability proof for the HMM, when it is applied to long time wave propagation problems.
We propose an efficient Markov Chain Monte Carlo method for sampling equilibrium distributions for stochastic lattice models. The method is capable of handling correctly and efficiently long and short-range particle i...
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ISBN:
(纸本)9783642219429
We propose an efficient Markov Chain Monte Carlo method for sampling equilibrium distributions for stochastic lattice models. The method is capable of handling correctly and efficiently long and short-range particle interactions. The proposed method is a Metropolis-type algorithm with the proposal probability transition matrix based on the coarse-grained approximating measures introduced in (Katsoulakis et al. Proc. Natl. Acad. Sci. 100(3):782-787, 2003;Katsoulakis et al. ESAIM-Math. Model. Numer. Anal. 41(3):627-660, 2007). The proposed algorithm reduces the computational cost due to energy differences and has comparable mixing properties with the classical microscopic Metropolis algorithm, controlled by the level of coarsening and reconstruction procedure. The properties and effectiveness of the algorithm are demonstrated with an exactly solvable example of a one dimensional Ising-type model, comparing efficiency of the single spin-flip Metropolis dynamics and the proposed coupled Metropolis algorithm.
Force-based multiphysics coupling methods have become popular since they provide a simple and efficient coupling mechanism, avoiding the difficulties in formulating and implementing a consistent coupling energy. They ...
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ISBN:
(纸本)9783642219429
Force-based multiphysics coupling methods have become popular since they provide a simple and efficient coupling mechanism, avoiding the difficulties in formulating and implementing a consistent coupling energy. They are also the only known pointwise consistent methods for coupling a general atomistic model to a finite element continuum model. However, the development of efficient and reliable iterative solution methods for the force-based approximation presents a challenge due to the non-symmetric and indefinite structure of the linearized force-based quasicontinuum approximation, as well as to its unusual stability properties. In this paper, we present rigorous numerical analysis and computational experiments to systematically study the stability and convergence rate for a variety of linear stationary iterative methods.
A method for calibrating a jump-diffusion model to observed option prices is presented. The calibration problem is formulated as an optimal control problem, with the model parameters as the control variable. It is wel...
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ISBN:
(纸本)9783642219429
A method for calibrating a jump-diffusion model to observed option prices is presented. The calibration problem is formulated as an optimal control problem, with the model parameters as the control variable. It is well known that such problems are ill-posed and need to be regularized. A Hamiltonian system, with non-differentiable Hamiltonian, is obtained from the characteristics of the corresponding Hamilton-Jacobi-Bellman equation. An explicit regularization of the Hamiltonian is suggested, and the regularized Hamiltonian system is solved with a symplectic Euler method. The paper is concluded with some numerical experiments on real and artificial data.
This work generalizes a multilevel forward Euler Monte Carlo method introduced in Michael B. Giles. (Michael Giles. Oper. Res. 56(3):607-617, 2008.) for the approximation of expected values depending on the solution t...
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ISBN:
(纸本)9783642219429
This work generalizes a multilevel forward Euler Monte Carlo method introduced in Michael B. Giles. (Michael Giles. Oper. Res. 56(3):607-617, 2008.) for the approximation of expected values depending on the solution to an Ito stochastic differential equation. The work (Michael Giles. Oper. Res. 56(3):607-617, 2008.) proposed and analyzed a forward Euler multilevel Monte Carlo method based on a hierarchy of uniform time discretizations and control variates to reduce the computational effort required by a standard, single level, Forward Euler Monte Carlo method. This work introduces an adaptive hierarchy of non uniform time discretizations, generated by an adaptive algorithm introduced in (Anna Dzougoutov et al. Raul Tempone. Adaptive Monte Carlo algorithms for stopped diffusion. In Multiscale methods in science and engineering, volume 44 of Lect. notes Comput. Sci. Eng., pages 59-88. Springer, Berlin, 2005;Kyoung-Sook Moon et al. Stoch. Anal. Appl. 23(3):511-558, 2005;Kyoung-Sook Moon et al. An adaptive algorithm for ordinary, stochastic and partial differential equations. In Recent advances in adaptive computation, volume 383 of Contemp. Math., pages 325-343. Amer. Math. Soc., Providence, RI, 2005.). This form of the adaptive algorithm generates stochastic, path dependent, time steps and is based on a posteriori error expansions first developed in (Anders Szepessy et al. Comm. Pure Appl. Math. 54(10):1169-1214, 2001). Our numerical results for a stopped diffusion problem, exhibit savings in the computational cost to achieve an accuracy of G(TOL), from G(TOL-3) using a single level version of the adaptive algorithm to G((TOL-1 log (TOL))(2)).
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