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Nonlinear Finite Elements For Continua And Structures

The objective of this work is to describe the design and implementation of a framework for building multi-disciplinary finite element programs. The main goals are generality, reusability, extendibility, good performance and memory efficiency. Another objective is preparing the code structure for team development to ensure the easy collaboration of experts in different fields in the development of multi-disciplinary applications. Kratos, the framework described in this work, contains several tools for the easy implementation of finite element applications and also provides a common platform for the natural interaction of different applications. To achieve this, an innovative variable base interface is designed and implemented. This interface is used at different levels of abstraction and showed to be very clear and extendible. A very efficient and flexible data structure and an extensible IO are created to overcome difficulties in dealing with multi-disciplinary problems. Several other concepts in existing works are also collected and adapted to coupled problems. The use of an interpreter, of different data layouts and variable number of dofs per node are examples of such approach. In order to minimize the possible conflicts arising in the development, a kernel and application approach is used. The code is structured in layers to reflect the working space of developers with different fields of expertise. Details are given on the approach chosen to increase performance and efficiency. Examples of application of Kratos to different multidisciplinary problems are presented in order to demonstrate the applicability and efficiency of the new object oriented environment.

/pdf/an-object-oriented-environment-for-developing-finite-element-4u7mzk1j18.pdf

An Object-oriented Environment for Developing Finite Element Codes for Multi-disciplinary Applications

By Lipman Bers London : Chapman and Hall Ltd. Pp. xv + 164. Price 62s. In the preface to this, the third volume in Surveys in Applied Mathematics, F. J. Weyl the Director of the Mathematical Sciences Division of the Office of Naval Research gives broadly speaking two aims as the basis for the series. These are (i) the need to make readily available up-to-date results in selected areas of research and (ii) the need to relate contributions from both sides of the iron curtain in order to produce a balanced appreciation of the present state of knowledge in any such area.

https://iopscience.iop.org/article/10.1088/0031-9112/10/5/018/pdf

Mathematical Aspects of Subsonic and Transonic Gas Dynamics

Current work presents a monolithic method for the solution of fluid–structure interaction problems involving flexible structures and free-surface flows. The technique presented is based upon the utilization of a Lagrangian description for both the fluid and the structure. A linear displacement–pressure interpolation pair is used for the fluid whereas the structure utilizes a standard displacement-based formulation. A slight fluid compressibility is assumed that allows to relate the mechanical pressure to the local volume variation. The method described features a global pressure condensation which in turn enables the definition of a purely displacement-based linear system of equations. A matrix-free technique is used for the solution of such linear system, leading to an efficient implementation. The result is a robust method which allows dealing with FSI problems involving arbitrary variations in the shape of the fluid domain. The method is completely free of spurious added-mass effects.

https://www.cimne.com/pfem/docs/2010_4.pdf

A monolithic Lagrangian approach for fluid–structure interaction problems

Numerical simulation of undrained insertion problems in geotechnical engineering with the Particle Finite Element Method (PFEM)

https://upcommons.upc.edu/bitstream/handle/2117/12768/5790979.pdf;sequence=1

Migration of a generic multi-physics framework to HPC environments

Creating a highly parallelizable code is a challenge and development for distributed memory machines (DMMs) can be very different form developing a serial code in term of algorithms and structure. For this reason, many developers in the field prefer to develop their own code from scratch. However, for an already existing framework with large development background the idea of transformation becomes attractive in order to reuse the effort done during years of development. In this presentation we explain how a relatively complex framework but with modular structure can be prepared for high performance computing with minimum modification. Kratos Multi-Physics [1] is an open source generic multi-disciplinary platform for solution of coupled problems consist of fluid, structure, thermal and electromagnetic fields. The parallelization of this framework is performed with objective of enforcing the less possible changes to its different solver modules and encapsulate the changes as much as possible in its common kernel. This objective is achieved thanks to the Kratos design and also innovative way of dealing with data transfers for a multi-disciplinary code. This work is completed by the migration of the framework from the x86 architecture to the Marenostrum Supercomputing platform. The migration has been verified by a set of benchmarks which show very good scalability, from which we present the Telescope problem in this paper.

We present an efficient technique for the solution of free surface flow problems using level set and a parallel edge-based finite elementmethod. An unstructured semi-explicit solution scheme is proposed. A custom data structure, obtained by blending node-based and edge-based approaches is presented so to allow a good parallel
performance. In addition to standard velocity extrapolation (for the convection of the level set function), an explicit extrapolation of the pressure field is performed in order to impose both the pressure boundary condition and the volume conservation. The latter is also improved with a modification of the divergence free constrain. The method is shown to allow an efficient solution of both simple benchmark cases and complex industrial examples.

An efficient edge-based level set finite element method for free surface flow problems

SUMMARY

The solution of problems in computational fluid dynamics (CFD) represents a classical field for the application of advanced numerical methods. Many different approaches were developed over the years to address CFD applications. Good examples are finite volumes, finite differences (FD), and finite elements (FE) but also newer approaches such as the lattice-Boltzmann (LB), smooth particle hydrodynamics or the particle finite element method. FD and LB methods on regular grids are known to be superior in terms of raw computing speed, but using such regular discretization represents an important limitation in dealing with complex geometries. Here, we concentrate on unstructured approaches which are less common in the GPU world. We employ a nonstandard FE approach which leverages an optimized edge-based data structure allowing a highly parallel implementation. Such technique is applied to the ‘convection-diffusion’ problem, which is often considered as a first step towards CFD because of similarities to the nonconservative form of the Navier–Stokes equations. In this regard, an existing highly optimized parallel OpenMP solver is ported to graphics hardware based on the OpenCL platform. The optimizations performed are discussed in detail. A number of benchmarks prove that the GPU-accelerated OpenCL code consistently outperforms the OpenMP version. Copyright © 2011 John Wiley & Sons, Ltd.

/pdf/opencl-based-implementation-of-an-unstructured-edge-based-1em5iuwez6.pdf

Pooyan Dadvand

Papers

An Object-oriented Environment for Developing Finite Element Codes for Multi-disciplinary Applications

Migration of a generic multi-physics framework to HPC environments

Migration of a generic multi-physics framework to HPC environments

An efficient edge-based level set finite element method for free surface flow problems

OpenCL‐based implementation of an unstructured edge‐based finite element convection‐diffusion solver on graphics hardware