Scientists working on mathematical models want to concentrate on the design of models. They pay l... more Scientists working on mathematical models want to concentrate on the design of models. They pay little attention to numerical methods such as the finite element method (FEM), their implementation and parallelization. The escript module in python provides an environment in which scientists can define new models using a language of partial differential equation (PDE) and spatial functions which is natural for the formulation of continuous models. This approach defines a high level of abstraction from the underlying data structures and frees modelers from issues of optimized implementation and parallelization. In its current implementation escript evaluates expressions which define PDE coefficients immediately for all nodes or elements of an FEM mesh. In the paper we will demonstrate that for complex rheologies such as the Drucker–Prager plasticity model, the memory requirements for this strategy are the limiting factor for scaling up the mesh size. The python module is backed by an escript C++ library where the processing is performed. We will discuss an new extension to the PDE coefficient handling provided by this C++ library which uses a lazy evaluation technique and will demonstrate the efficiency of this new extension in terms of compute time and memory usage for a practical engineering application, namely the simulation of elastic-plastic, saturated porous media.
Journal of Geophysical Research: Solid Earth, 2013
1] We present a linear instability analysis and numerical simulations describing deformation and ... more 1] We present a linear instability analysis and numerical simulations describing deformation and melt patterns in pure shear extension of a partly molten rock. Our models implement numerical techniques that enable strong strain localization and are applied to study melt-strain interactions during continental rifting. Our results show that instabilities can initiate with either strain localization or melt localization, followed by a coupled evolution of melt and shear bands driven by a strong melt-viscosity-shear feedback. This indicates that a local increase in melt fraction due to segregation and/or local melting promotes strain localization and may lead to the formation of large shear bands. Melt-shear interactions can therefore enable rifting where tectonic forces are not sufficient to induce melt-free rifting, resulting in lubricated faults, but not necessarily observed volcanism. Finally, our simulations reveal significant asymmetry in melt segregation around localized shear bands, providing new insights into melt distribution across rift boundary faults and other extensional structures. Citation: Mohajeri, A., Y. Finzi, H. Muhlhaus, and G. Rosenbaum (2013), Melt and shear interactions in the lithosphere: Theory and numerical analysis of pure shear extension,
Springer Series in Geomechanics and Geoengineering, 2011
The understanding of chemical effects on mechanical behavior of porous media is a key element in ... more The understanding of chemical effects on mechanical behavior of porous media is a key element in the solution of problems in geology, mining, soil, rock and environmental engineering. In order to develop this understanding, the current work employs a new set of equations to numerically investigate the coupled mechanicalhydrological-chemical (MHC) problem for soils and soft rocks. The objectives of this research are to observe the soil and soft rock behavior under mechanical loading and chemical erosion and also to validate the application of our solver algorithm written in a finite element programming environment "escript".
Scientists working on mathematical models want to concentrate on the design of models. They pay l... more Scientists working on mathematical models want to concentrate on the design of models. They pay little attention to numerical methods such as the finite element method (FEM), their implementation and parallelization. The escript module in python provides an environment in which scientists can define new models using a language of partial differential equation (PDE) and spatial functions which is natural for the formulation of continuous models. This approach defines a high level of abstraction from the underlying data structures and frees ...
Scientists working on mathematical models want to concentrate on the design of models. They pay l... more Scientists working on mathematical models want to concentrate on the design of models. They pay little attention to numerical methods such as the finite element method (FEM), their implementation and parallelization. The escript module in python provides an environment in which scientists can define new models using a language of partial differential equation (PDE) and spatial functions which is natural for the formulation of continuous models. This approach defines a high level of abstraction from the underlying data structures and frees modelers from issues of optimized implementation and parallelization. In its current implementation escript evaluates expressions which define PDE coefficients immediately for all nodes or elements of an FEM mesh. In the paper we will demonstrate that for complex rheologies such as the Drucker–Prager plasticity model, the memory requirements for this strategy are the limiting factor for scaling up the mesh size. The python module is backed by an escript C++ library where the processing is performed. We will discuss an new extension to the PDE coefficient handling provided by this C++ library which uses a lazy evaluation technique and will demonstrate the efficiency of this new extension in terms of compute time and memory usage for a practical engineering application, namely the simulation of elastic-plastic, saturated porous media.
Journal of Geophysical Research: Solid Earth, 2013
1] We present a linear instability analysis and numerical simulations describing deformation and ... more 1] We present a linear instability analysis and numerical simulations describing deformation and melt patterns in pure shear extension of a partly molten rock. Our models implement numerical techniques that enable strong strain localization and are applied to study melt-strain interactions during continental rifting. Our results show that instabilities can initiate with either strain localization or melt localization, followed by a coupled evolution of melt and shear bands driven by a strong melt-viscosity-shear feedback. This indicates that a local increase in melt fraction due to segregation and/or local melting promotes strain localization and may lead to the formation of large shear bands. Melt-shear interactions can therefore enable rifting where tectonic forces are not sufficient to induce melt-free rifting, resulting in lubricated faults, but not necessarily observed volcanism. Finally, our simulations reveal significant asymmetry in melt segregation around localized shear bands, providing new insights into melt distribution across rift boundary faults and other extensional structures. Citation: Mohajeri, A., Y. Finzi, H. Muhlhaus, and G. Rosenbaum (2013), Melt and shear interactions in the lithosphere: Theory and numerical analysis of pure shear extension,
Springer Series in Geomechanics and Geoengineering, 2011
The understanding of chemical effects on mechanical behavior of porous media is a key element in ... more The understanding of chemical effects on mechanical behavior of porous media is a key element in the solution of problems in geology, mining, soil, rock and environmental engineering. In order to develop this understanding, the current work employs a new set of equations to numerically investigate the coupled mechanicalhydrological-chemical (MHC) problem for soils and soft rocks. The objectives of this research are to observe the soil and soft rock behavior under mechanical loading and chemical erosion and also to validate the application of our solver algorithm written in a finite element programming environment "escript".
Scientists working on mathematical models want to concentrate on the design of models. They pay l... more Scientists working on mathematical models want to concentrate on the design of models. They pay little attention to numerical methods such as the finite element method (FEM), their implementation and parallelization. The escript module in python provides an environment in which scientists can define new models using a language of partial differential equation (PDE) and spatial functions which is natural for the formulation of continuous models. This approach defines a high level of abstraction from the underlying data structures and frees ...
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Papers by Arash Mohajeri