Multiscale Computing Research Articles

Performance of distributed multiscale simulations.

Multiscale simulations model phenomena across natural scales using monolithic or component-based code, running on local or distributed resources. In this work, we investigate the performance of distributed multiscale computing of component-based models, guided by six multiscale applications with different characteristics and from several disciplines. Three modes of distributed multiscale computing are identified: supplementing local dependencies with large-scale resources, load distribution over multiple resources, and load balancing of small- and large-scale resources. We find that the first mode has the apparent benefit of increasing simulation speed, and the second mode can increase simulation speed if local resources are limited. Depending on resource reservation and model coupling topology, the third mode may result in a reduction of resource consumption.

Foundations of distributed multiscale computing: Formalization, specification, and analysis

Inherently complex problems from many scientific disciplines require a multiscale modeling approach. Yet its practical contents remain unclear and inconsistent. Moreover, multiscale models can be very computationally expensive, and may have potential to be executed on distributed infrastructure. In this paper we propose firm foundations for multiscale modeling and distributed multiscale computing. Useful interaction patterns of multiscale models are made predictable with a submodel execution loop (SEL), four coupling templates, and coupling topology properties. We enhance a high-level and well-defined Multiscale Modeling Language (MML) that describes and specifies multiscale models and their computational architecture in a modular way. The architecture is analyzed using directed acyclic task graphs, facilitating validity checking, scheduling distributed computing resources, estimating computational costs, and predicting deadlocks. Distributed execution using the multiscale coupling library and environment (MUSCLE) is outlined. The methodology is applied to two selected applications in nanotechnology and biophysics, showing its capabilities.

Multiscale Computing with the Multiscale Modeling Library and Runtime Environment

We introduce a software tool to simulate multiscale models: the Multiscale Coupling Library and Environment 2 (MUSCLE 2). MUSCLE 2 is a component-based modeling tool inspired by the multiscale modeling and simulation framework, with an easy-to-use API which supports Java, C++, C, and Fortran. We present MUSCLE 2's runtime features, such as its distributed computing capabilities, and its benefits to multiscale modelers. We also describe two multiscale models that use MUSCLE 2 to do distributed multiscale computing: an in-stent restenosis and a canal system model. We conclude that MUSCLE 2 is a notable improvement over the previous version of MUSCLE, and that it allows users to more flexibly deploy simulations of multiscale models, while improving their performance.

A Distributed Multiscale Computation of a Tightly Coupled Model Using the Multiscale Modeling Language

Nature is observed at all scales; with multiscale modeling, scientists bring together several scales for a holistic analysis of a phenomenon. The models on these different scales may require significant but also heterogeneous computational resources, creating the need for distributed multiscale computing. A particularly demanding type of multiscale models, tightly coupled, brings with it a number of theoretical and practical issues. In this contribution, a tightly coupled model of in-stent restenosis is first theoretically examined for its multiscale merits using the Multiscale Modeling Language (MML); this is aided by a toolchain consisting of MAPPER Memory (MaMe), the Multiscale Application Designer (MAD), and Gridspace Experiment Workbench. It is implemented and executed with the general Multiscale Coupling Library and Environment (MUSCLE). Finally, it is scheduled amongst heterogeneous infrastructures using the QCG-Broker. This marks the first occasion that a tightly coupled application uses distributed multiscale computing in such a general way.

Multiscale computations for carbon nanotubes based on a hybrid QM/QC (quantum mechanical and quasicontinuum) approach

An effective multiscale computing scheme based on QM/QC (quantum mechanics/quasicontinuum) is applied for simulation of Carbon nanotubes (CNTS) mechanics. First, quasicontinuum simulation of deformations of curved crystalline structures is conducted to examine the fully nonlocal behavior of CNTs with the aid of high-order interpolation functions and the “cluster” concept, which facilitates accurate energy approximation for crystals. Next, a multiscale computing approach based on QM/QC hybridization is devised, and applied for simulation of CNT mechanics. The bonding configuration changes, e.g. bond breaking or creation, near defect sites are correctly represented with the QM/QC hybrid model. For studying electronic properties coupled with the mechanical deformation of CNTs, the change of the electrical properties from an initial semiconductor into metal under mechanical bending is investigated. Single-walled CNTs having various types of defects and subjected to uniaxial tension are considered for fracture. The theoretical strength of the CNTs in the presence of each defect is computed based on the QM/QC hybrid scheme, wherein the defect neighborhood is modeled as a QM zone for a first-principle-based calculation using density functional theory (DFT), and the remaining area as a QC zone. This multiscale computing approach greatly improves the accuracy in the prediction of the failure strains of CNTs over a purely molecular mechanical or quasicontinuum method.

Accuracy and Stability of the Coarse Time-Stepper for a Lattice Boltzmann Model

The equation-free framework for multiscale computing is built around the central idea of a coarse time-stepper, which is an approximate time integrator for the unavailable macroscopic model when only a microscopic simulator is given. In this paper, we study the numerical properties of the coarse time-stepper when a lattice Boltzmann model for one-dimensional diffusion is used as the microscopic simulator. We derive analytical expressions for the accuracy and stability of the coarse time-stepper, which allow us to study the influence of various aspects involved in its construction.

Accelerating the coarse time‐stepper for a lattice Boltzmann model

AbstractThe equation‐free framework for multiscale computing is built around the central idea of a coarse time‐stepper, which is an approximate time integrator for the macroscopic variables when only a microscopic simulator is available. In a previous paper, we studied the accuracy and stability of the coarse time‐stepper when the microscopic simulator is a lattice Boltzmann model for one‐dimensional diffusion. In this paper, we rely on these results to show how the coarse time‐stepper can be accelerated using the recently proposed teleprojective method or the multistep state extrapolation method. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Concurrent Multiscale Computing of Deformation Microstructure by Relaxation and Local Enrichment with Application to Single‐Crystal Plasticity

This paper is concerned with the effective modeling of deformation microstructures within a concurrent multiscale computing framework. We present a rigorous formulation of concurrent multiscale computing based on relaxation; we establish the connection between concurrent multiscale computing and enhanced‐strain elements; and we illustrate the approach in an important area of application, namely, single‐crystal plasticity, for which the explicit relaxation of the problem is derived analytically. This example demonstrates the vast effect of microstructure formation on the macroscopic behavior of the sample, e.g., on the force/travel curve of a rigid indentor. Thus, whereas the unrelaxed model results in an overly stiff response, the relaxed model exhibits a proper limit load, as expected. Our numerical examples additionally illustrate that ad hoc element enhancements, e.g., based on polynomial, trigonometric, or similar representations, are unlikely to result in any significant relaxation in general.

A Quasicontinuum Method for Deformations of Carbon Nanotubes

We present a coarse-graining computation for deformations of CNTs (carbon nanotubes) via QC (quasicontinuum), particularly targeting analysis of multi-walled carbon nanotubes. Higher order triangular elements are utilized for proper interpolation of atom po- sitions of the CNT on the basis of QC approach. The computing scheme enables one to differentiate between the fully atomistic zone and the coarse-grained zone in the framework of the multiscale computing. Several nu- merical examples demonstrate the effectiveness and ac- curacy of the present methodology.

Multiscale computing.

Multiscale computing (MSC) involves the computation, manipulation, and analysis of information at different resolution levels. Widespread use of MSC algorithms and the discovery of important relationships between different approaches to implementation were catalyzed, in part, by the recent interest in wavelets. We present two examples that demonstrate how MSC can help scientists understand complex data. The first is from acoustical signal processing and the second is from computer graphics.

Numerical Computation of Rank-One Convex Envelopes

We describe an algorithm for the numerical computation of the rank-one convex envelope of a function $f:\MM^{m\times n}\rightarrow\RR$. We prove its convergence and an error estimate in $L^\infty$.