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Albany: Using Component-based Design to Develop a Flexible, Generic Multiphysics Analysis Code
Abstract:
Albany is a multiphysics code constructed by assembling a set of reusable, general components. It is an implicit, unstructured grid finite element code that hosts a set of advanced features that are readily combined within a single analysis run. Albany uses template-based generic programming methods to provide extensibility and flexibility; it employs a generic residual evaluation interface to support the easy addition and modification of physics. This interface is coupled to powerful automatic differentiation utilities that are used to implement efficient nonlinear solvers and preconditioners, and also to enable sensitivity analysis and embedded uncertainty quantification capabilities as part of the forward solve. The flexible application programming interfaces in Albany couple to two different adaptive mesh libraries; it internally employs generic integration machinery that supports tetrahedral, hexahedral, and hybrid meshes of user specified order. We present the overall design of Albany, and focus on the specifics of the integration of many of its advanced features. As Albany and the components that form it are openly available on the internet, it is our goal that the reader might find some of the design concepts useful in their own work. Albany results in a code that enables the rapid development of parallel, numerically efficient multiphysics software tools. In discussing the features and details of the integration of many of the components involved, we show the reader the wide variety of solution components that are available and what is possible when they are combined within a simulation capability.
Key Words: partial differential equations, finite element analysis, template-based generic programmin
Multidisciplinary Design Optimization of an Aircraft Wing via a Matrix-Free Approach
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/140437/1/6.2014-2429.pd
Data-driven modelling of biological multi-scale processes
Biological processes involve a variety of spatial and temporal scales. A
holistic understanding of many biological processes therefore requires
multi-scale models which capture the relevant properties on all these scales.
In this manuscript we review mathematical modelling approaches used to describe
the individual spatial scales and how they are integrated into holistic models.
We discuss the relation between spatial and temporal scales and the implication
of that on multi-scale modelling. Based upon this overview over
state-of-the-art modelling approaches, we formulate key challenges in
mathematical and computational modelling of biological multi-scale and
multi-physics processes. In particular, we considered the availability of
analysis tools for multi-scale models and model-based multi-scale data
integration. We provide a compact review of methods for model-based data
integration and model-based hypothesis testing. Furthermore, novel approaches
and recent trends are discussed, including computation time reduction using
reduced order and surrogate models, which contribute to the solution of
inference problems. We conclude the manuscript by providing a few ideas for the
development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and
Multiscale Dynamics (American Scientific Publishers
A Scalable Parallel Approach for High-Fidelity Aerostructural Analysis and Optimization
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97076/1/AIAA2012-1922.pd
Parametric Level Set Methods for Inverse Problems
In this paper, a parametric level set method for reconstruction of obstacles
in general inverse problems is considered. General evolution equations for the
reconstruction of unknown obstacles are derived in terms of the underlying
level set parameters. We show that using the appropriate form of parameterizing
the level set function results a significantly lower dimensional problem, which
bypasses many difficulties with traditional level set methods, such as
regularization, re-initialization and use of signed distance function.
Moreover, we show that from a computational point of view, low order
representation of the problem paves the path for easier use of Newton and
quasi-Newton methods. Specifically for the purposes of this paper, we
parameterize the level set function in terms of adaptive compactly supported
radial basis functions, which used in the proposed manner provides flexibility
in presenting a larger class of shapes with fewer terms. Also they provide a
"narrow-banding" advantage which can further reduce the number of active
unknowns at each step of the evolution. The performance of the proposed
approach is examined in three examples of inverse problems, i.e., electrical
resistance tomography, X-ray computed tomography and diffuse optical
tomography
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