30 results found
Buchan AG, Farrell PE, Gorman GJ, et al., 2014, The immersed body supermeshing method for modelling reactor physics problems with complex internal structures, ANNALS OF NUCLEAR ENERGY, Vol: 63, Pages: 399-408, ISSN: 0306-4549
This article describes a new immersed body method for the efficient modelling of complex reactor physics problems. The approach is based on a projection method that maps geometric diagnostics of internal bodies onto practical computational meshes. It applies a recently developed supermeshing algorithm originally developed for data transfer problems to parameterise the effects of internal bodies on the reactor dynamics. This projects meshes of internal bodies onto a mesh that encompasses the entire problem domain. With this mapping, all necessary information about the intersection of an element with the internal body is known. This includes information about the volume, surface area and distances along the internal bodies; importantly, these quantities are always conserved. The appropriate material cross-sections for each element are then calculated from the volume information to account for all the internal bodies they contain. This in turn enables the problem to be solved efficiently on meshes that are practical to generate. The method is demonstrated on two eigenvalue problems where the domain contains fuel pins, cooling pipes, control rods and guide tubes. The first problem is used to demonstrate convergence when the mesh fully resolves the internal bodies and the geometric details of the problem are completely recovered. The second problem models the SUPO (Super POwer) solution reactor which contains many complex and detailed internal components. It is shown that the internal structures of the problem can be parameterised efficiently without the use of computationally expensive geometry-conforming meshes. © 2013 Elsevier Ltd. All rights reserved.
Farrell PE, Cotter CJ, Funke SW, et al., 2014, A FRAMEWORK FOR THE AUTOMATION OF GENERALIZED STABILITY THEORY, SIAM JOURNAL ON SCIENTIFIC COMPUTING, Vol: 36, Pages: C25-C48, ISSN: 1064-8275
Funke SW, Farrell PE, Piggott MD, et al., 2014, Tidal turbine array optimisation using the adjoint approach, RENEWABLE ENERGY, Vol: 63, Pages: 658-673, ISSN: 0960-1481
Oceanic tides have the potential to yield a vast amount of renewable energy. Tidal stream generators are one of the key technologies for extracting and harnessing this potential. In order to extract an economically useful amount of power, hundreds of tidal turbines must typically be deployed in an array. This naturally leads to the question of how these turbines should be configured to extract the maximum possible power: the positioning and the individual tuning of the turbines could significantly influence the extracted power, and hence is of major economic interest. However, manual optimisation is difficult due to legal site constraints, nonlinear interactions of the turbine wakes, and the cubic dependence of the power on the flow speed. The novel contribution of this paper is the formulation of this problem as an optimisation problem constrained by a physical model, which is then solved using an efficient gradient-based optimisation algorithm. In each optimisation iteration, a two-dimensional finite element shallow water model predicts the flow and the performance of the current array configuration. The gradient of the power extracted with respect to the turbine positions and their tuning parameters is then computed in a fraction of the time taken for a flow solution by solving the associated adjoint equations. These equations propagate causality backwards through the computation, from the power extracted back to the turbine positions and the tuning parameters. This yields the gradient at a cost almost independent of the number of turbines, which is crucial for any practical application. The utility of the approach is demonstrated by optimising turbine arrays in four idealised scenarios and a more realistic case with up to 256 turbines in the Inner Sound of the Pentland Firth, Scotland. © 2013 The Authors.
Hiester HR, Piggott MD, Farrell PE, et al., 2014, Assessment of spurious mixing in adaptive mesh simulations of the two-dimensional lock-exchange, OCEAN MODELLING, Vol: 73, Pages: 30-44, ISSN: 1463-5003
Numerical simulations are used to evaluate the impact of adaptive meshes on the two-dimensional lock-exchange flow. In particular, the diapycnal mixing is quantified through calculation of the background potential energy. The choice of metric, which guides the mesh adapt, is fundamental to the success of an adaptive mesh simulation. The performance of different Hessian-based metrics is assessed and cases that both outperform and underperform, compared to fixed mesh simulations, are evaluated. The differences in performance result from the different forms of the metric and the extent to which smaller-scale fluctuations can influence the adapted mesh. The best performing metric produces levels of diapycnal mixing that are comparable to high resolution fixed mesh simulations that use one to two orders of magnitude more mesh vertices. Comparison of the mixing with the numerical simulations of Özgökmen et al. (2007) also demonstrates the validity of the adaptive mesh simulations. © 2013 Elsevier Ltd.
Baker CMJ, Buchan AG, Pain CC, et al., 2013, Multimesh anisotropic adaptivity for the Boltzmann transport equation, ANNALS OF NUCLEAR ENERGY, Vol: 53, Pages: 411-426, ISSN: 0306-4549
This article presents a new adaptive finite element based method for the solution of the spatial dimensions of the Boltzmann transport equation. The method applies a curvature based error metric to locate the under and over resolved regions of a solution and this, in turn, is used to guide the refinement and coarsening of the spatial mesh. The error metrics and re-meshing procedures are designed such that they enable anisotropic resolution to form in the mesh should it be appropriate to do so. The adaptive mesh enables the appropriate resolution to be applied throughout the whole domain of a problem and so increase the efficiency of the solution procedure. Another new approach is also described that allows independent adaptive meshes to form for each of the energy group fluxes. The use of independent meshes can significantly improve computational efficiency when solving problems where the different group fluxes require high resolution over different regions. The mesh to mesh interpolation is made possible through the use of a ‘supermeshing’ procedure that ensures the conservation of particles when calculating the group to group scattering sources. Finally it is shown how these methods can be incorporated within a solver to resolve both fixed source and eigenvalue problems. A selection of both fixed source and eigenvalue problems are solved in order to demonstrate the capabilities of these methods.
Farrell PE, Ham DA, Funke SW, et al., 2013, AUTOMATED DERIVATION OF THE ADJOINT OF HIGH-LEVEL TRANSIENT FINITE ELEMENT PROGRAMS, SIAM JOURNAL ON SCIENTIFIC COMPUTING, Vol: 35, Pages: C369-C393, ISSN: 1064-8275
In this paper we demonstrate a new technique for deriving discrete adjoint and tangent linear models of a finite element model. The technique is significantly more efficient and automatic than standard algorithmic differentiation techniques. The approach relies on a high-level symbolic representation of the forward problem. In contrast to developing a model directly in Fortran or C++, high-level systems allow the developer to express the variational problems to be solved in near-mathematical notation. As such, these systems have a key advantage: since the mathematical structure of the problem is preserved, they are more amenable to automated analysis and manipulation. The framework introduced here is implemented in a freely available software package named dolfin-adjoint, based on the FEniCS Project. Our approach to automated adjoint derivation relies on run-time annotation of the temporal structure of the model and employs the FEniCS finite element form compiler to automatically generate the low-level code for the derived models. This approach requires only trivial changes to a large class of forward models, including complicated time-dependent nonlinear models. The adjoint model automatically employs optimal checkpointing schemes to mitigate storage requirements for nonlinear models, without any user management or intervention. Furthermore, both the tangent linear and adjoint models naturally work in parallel, without any need to differentiate through calls to MPI or to parse OpenMP directives. The generality, applicability, and efficiency of the approach are demonstrated with examples from a wide range of scientific applications. © 2013 Society for Industrial and Applied Mathematics.
Maddison JR, Cotter CJ, Farrell PE, 2013, Geostrophic balance preserving interpolation in mesh adaptive linearised shallow-water ocean modelling (vol 37, pg 35, 2011), OCEAN MODELLING, Vol: 68, Pages: 106-106, ISSN: 1463-5003
Milthaler FFM, Pavlidis D, Xiang J, et al., 2013, THE IMMERSED BODY METHOD COMBINED WITH MESH ADAPTIVITY FOR FLUID-SOLID COUPLING, 6th International Conference on Coastal Structures, Publisher: WORLD SCIENTIFIC PUBL CO PTE LTD, Pages: 277-283
Farrell PE, Funke SW, Ham DA, et al., 2012, dolfin-adjoint
The dolfin-adjoint project automatically derives the discrete adjoint and tangent linear models from a forward finite element model written in the Python interface to Dolfin.
Gorman GJ, Southern J, Farrell PE, et al., 2012, Hybrid OpenMP/MPI anisotropic mesh smoothing, International Conference on Computational Science (ICCS), Publisher: ELSEVIER SCIENCE BV, Pages: 1513-1522, ISSN: 1877-0509
Mesh smoothing is an important algorithm for the improvement of element quality in unstructured mesh finite element methods. A new optimisation based mesh smoothing algorithm is presented for anisotropic mesh adaptivity. It is shown that this smoothing kernel is very effective at raising the minimum local quality of the mesh. A number of strategies are employed to reduce the algorithm's cost while maintaining its effectiveness in improving overall mesh quality. The method is parallelised using hybrid OpenMP/MPI programming methods, and graph colouring to identify independent sets. Different approaches are explored to achieve good scaling performance within a shared memory compute node. © 2012 Published by Elsevier Ltd.
Maddison JR, Farrell PE, Maddison JR, et al., 2012, Directional integration on unstructured meshes via supermesh construction, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 231, Pages: 4422-4432, ISSN: 0021-9991
Southern J, Gorman GJ, Piggott MD, et al., 2012, Parallel anisotropic mesh adaptivity with dynamic load balancing for cardiac electrophysiology, JOURNAL OF COMPUTATIONAL SCIENCE, Vol: 3, Pages: 8-16, ISSN: 1877-7503
Simulations in cardiac electrophysiology generally use very fine meshes and small time steps to resolve highly localized wavefronts. This expense motivates the use of mesh adaptivity, which has been demonstrated to reduce the overall computational load. However, even with mesh adaptivity performing such simulations on a single processor is infeasible. Therefore, the adaptivity algorithm must be parallelised. Rather than modifying the sequential adaptive algorithm, the parallel mesh adaptivity method introduced in this paper focuses on dynamic load balancing in response to the local refinement and coarsening of the mesh. In essence, the mesh partition boundary is perturbed away from mesh regions of high relative error, while also balancing the computational load across processes. The parallel scaling of the method when applied to physiologically realistic heart meshes is shown to be good as long as there are enough mesh nodes to distribute over the available parallel processes. It is shown that the new method is dominated by the cost of the sequential adaptive mesh procedure and that the parallel overhead of inter-process data migration represents only a small fraction of the overall cost. © 2011.
Vire A, Xiang J, Milthaler F, et al., 2012, Modelling of fluid-solid interactions using an adaptive mesh fluid model coupled with a combined finite-discrete element model, OCEAN DYNAMICS, Vol: 62, Pages: 1487-1501, ISSN: 1616-7341
Fluid-structure interactions are modelled by coupling the finite element fluid/ocean model 'Fluidity- ICOM' with a combined finite-discrete element solid model 'Y3D'. Because separate meshes are used for the fluids and solids, the present method is flexible in terms of discretisation schemes used for each material. Also, it can tackle multiple solids impacting on one another, without having ill-posed problems in the resolution of the fluid's equations. Importantly, the proposed approach ensures that Newton's third law is satisfied at the discrete level. This is done by first computing the action-reaction force on a supermesh, i.e. a function superspace of the fluid and solid meshes, and then projecting it to both meshes to use it as a source term in the fluid and solid equations. This paper demonstrates the properties of spatial conservation and accuracy of the method for a sphere immersed in a fluid, with prescribed fluid and solid velocities. While spatial conservation is shown to be independent of the mesh resolutions, accuracy requires fine resolutions in both fluid and solid meshes. It is further highlighted that unstructured meshes adapted to the solid concentration field reduce the numerical errors, in comparison with uniformly structured meshes with the same number of elements. The method is verified on flow past a falling sphere. Its potential for ocean applications is further shown through the simulation of vortex-induced vibrations of two cylinders and the flow past two flexible fibres. © 2012 Springer-Verlag.
Farrell PE, Farrell PE, Farrell PE, 2011, The addition of fields on different meshes, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 230, Pages: 3265-3269, ISSN: 0021-9991
Farrell PE, Maddison JR, Farrell PE, et al., 2011, Conservative interpolation between volume meshes by local Galerkin projection, COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, Vol: 200, Pages: 89-100, ISSN: 0045-7825
Farrell PE, Micheletti S, Perotto S, et al., 2011, An anisotropic Zienkiewicz-Zhu-type error estimator for 3D applications, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Vol: 85, Pages: 671-692, ISSN: 0029-5981
Farrell PE, Piggott MD, Gorman GJ, et al., 2011, Automated continuous verification for numerical simulation, GEOSCIENTIFIC MODEL DEVELOPMENT, Vol: 4, Pages: 435-449, ISSN: 1991-959X
Verification is a process crucially important for the final users of a computational model: code is useless if its results cannot be relied upon. Typically, verification is seen as a discrete event, performed once and for all after development is complete. However, this does not reflect the reality that many geoscientific codes undergo continuous development of the mathematical model, discretisation and software implementation. Therefore, we advocate that in such cases verification must be continuous and happen in parallel with development: the desirability of their automation follows immediately. This paper discusses a framework for automated continuous verification of wide applicability to any kind of numerical simulation. It also documents a range of test cases to show the possibilities of the framework. © 2011 Author(s).
Maddison JR, Cotter CJ, Farrell PE, et al., 2011, Geostrophic balance preserving interpolation in mesh adaptive linearised shallow-water ocean modelling, OCEAN MODELLING, Vol: 37, Pages: 35-48, ISSN: 1463-5003
Southern J, Gorman GJ, Piggott MD, et al., 2010, Anisotropic mesh adaptivity for cardiac electrophysiology, International Conference on Computational Science (ICCS), Publisher: ELSEVIER SCIENCE BV, Pages: 929-938, ISSN: 1877-0509
The simulation of cardiac electrophysiology requires small time steps and a fine mesh in order to resolve very sharp, but highly localized, wavefronts. The use of very high resolution meshes containing large numbers of nodes results in a high computational cost, both in terms of CPU hours and memory footprint. In this paper an anisotropic mesh adaptivity technique is implemented in the Chaste physiological simulation library in order to reduce the mesh resolution away from the depolarization front. Adapting the mesh results in a reduction in the number of degrees of freedom of the system to be solved by an order of magnitude during propagation and 2-3 orders of magnitude in the subsequent plateau phase. As a result, a computational speedup by a factor of between 5 and 12 has been obtained with no loss of accuracy, both in a slab-like geometry and for a realistic heart mesh with a spatial resolution of 0.125 mm. © 2010 Published by Elsevier Ltd.
Southern J, Gorman GJ, Piggott MD, et al., 2010, Simulating cardiac electrophysiology using anisotropic mesh adaptivity, JOURNAL OF COMPUTATIONAL SCIENCE, Vol: 1, Pages: 82-88, ISSN: 1877-7503
The simulation of cardiac electrophysiology requires small time steps and a fine mesh in order to resolve very sharp, but highly localized, wavefronts. The use of very high resolution meshes containing large numbers of nodes results in a high computational cost, both in terms of CPU hours and memory footprint. In this paper an anisotropic mesh adaptivity technique is implemented in the Chaste physiological simulation library in order to reduce the mesh resolution away from the depolarization front. Adapting the mesh results in a reduction in the number of degrees of freedom of the system to be solved by an order of magnitude during propagation and 2-3 orders of magnitude in the subsequent plateau phase. As a result, a computational speedup by a factor of between 5 and 12 has been obtained with no loss of accuracy, both in a slab-like geometry and for a realistic heart mesh with a spatial resolution of 0.125 mm. © 2010 Elsevier B.V. All rights reserved.
Fang F, Pain CC, Navon IM, et al., 2009, A POD reduced order unstructured mesh ocean modelling method for moderate Reynolds number flows, OCEAN MODELLING, Vol: 28, Pages: 127-136, ISSN: 1463-5003
Fang F, Pain CC, Navon IM, et al., 2009, A POD reduced-order 4D-Var adaptive mesh ocean modelling approach, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Vol: 60, Pages: 709-732, ISSN: 0271-2091
A novel proper orthogonal decomposition (POD) inverse model, developed for an adaptive mesh ocean model (the Imperial College Ocean Model, ICOM), is presented here. The new POD model is validated using the Munk gyre flow test case, where it inverts for initial conditions. The optimized velocity fields exhibit overall good agreement with those generated by the full model. The correlation between the inverted and the true velocity is 80-98% over the majority of the domain. Error estimation was used to judge the quality of reduced-order adaptive mesh models. The cost function is reduced by 20% of its original value, and further by 70% after the POD bases are updated. In this study, the reduced adjoint model is derived directly from the discretized reduced forward model. The whole optimization procedure is undertaken completely in reduced space. The computational cost for the four-dimensional variational (4D-Var) data assimilation is significantly reduced (here a decrease of 70% in the test case) by decreasing the dimensional size of the control space, in both the forward and adjoint models. Computational efficiency is further enhanced since both the reduced forward and adjoint models are constructed by a series of time-independent sub-matrices. The reduced forward and adjoint models can be run repeatedly with negligible computational costs. An adaptive POD 4D-Var is employed to update the POD bases as minimization advances and loses control, thus adaptive updating of the POD bases is necessary. Previously developed numerical approaches Fang et al. (Int. J. Numer. Meth. Fluids 2008) are employed to accurately represent the geostrophic balance and improve the efficiency of the POD simulation. Copyright © 2008 John Wiley & Sons, Ltd.
Farrell PE, Maddison JR, 2009, Interpolation between discontinuous volume meshes by local Galerkin projection, Publisher: CINME, Pages: 73-76-73-76
Farrell PE, Piggott MD, Pain CC, et al., 2009, Conservative interpolation between unstructured meshes via supermesh construction, COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, Vol: 198, Pages: 2632-2642, ISSN: 0045-7825
Mesh adaptivity on unstructured meshes is a proven and popular tool for reducing the computational cost of numerical simulations. Unstructured meshes are often preferred in mesh adaptivity as they allow for greater geometric flexibility and arbitrary anisotropy in resolving simulation features. However, such mesh adaptivity suffers from a significant drawback: the interpolation errors caused by interpolating from the old mesh to the new mesh typically destroys conservation of quantities important to the physical accuracy of the simulation (e.g., density, volume fraction, tracer concentration, etc.). This work presents several globally conservative interpolation operators between general unstructured meshes via the construction of an intermediate supermesh. The construction of the supermesh is performed by transforming the problem to the input to a constrained meshing problem. The performance of the conservative interpolation operators are compared against interpolation using the underlying basis functions. © 2009 Elsevier B.V. All rights reserved.
Gorman GJ, Pain CC, Piggott MD, et al., 2009, Interleaved parallel tetrahedral mesh optimisation and dynamic load-balancing, Publisher: CINME, Pages: 101-104-101-104
Piggott MD, Farrell PE, Wilson CR, et al., 2009, Anisotropic mesh adaptivity for multi-scale ocean modelling, PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 367, Pages: 4591-4611, ISSN: 1364-503X
Research into the use of unstructured mesh methods in oceanography has been growing steadily over the past decade. The advantages of this approach for domain representation and non-uniform resolution are clear. However, a number of issues remain, in particular those related to the computational cost of models produced using unstructured mesh methods compared with their structured mesh counterparts. Mesh adaptivity represents an important means to improve the competitiveness of unstructured mesh models, where high resolution is only used when and where necessary. In this paper, an optimization-based approach to mesh adaptivity is described where emphasis is placed on capturing anisotropic solution characteristics. Comparisons are made between the results obtained with uniform isotropic resolution, isotropic adaptive resolution and fully anisotropic adaptive resolution.
Farrell PE, Gorman GJ, Piggott MD, 2008, Automated continuous code verification for the Imperial College Ocean Model, Halifax, Nova Scotia, Canada
Ham D, Farrell P, Gorman G, et al., 2008, Spud
Spud is a generic system for defining, writing and processing options files for scientific computer models.The interfaces to scientific computer models are frequently primitive, under-documented and ad-hoc text files. This makes using and developing the model in question difficult and error-prone.With Spud, the model developer need only write a rules file (schema) which defines the options which the model takes and the relationship between them. The Spud component Diamond then provides an automatically generated graphical user interface which guides the user and validates the user's input against the schema. Diamond writes out an xml options file for use in Spud.The developer then uses libspud to read the options file into the model. Libspud can read any valid options file without further code modifications and makes the options available at any point in the model code at which they are required.Spud further provides the facility for the schema to be self-documenting and Diamond presents this documentation to the model user in a context-sensitive manner.
Ham DA, Farrell PE, Gorman GJ, et al., 2008, Spud 1.0: generalising and automating the user interfaces of scientific computer models, GEOSCI MODEL DEV, Vol: 1, Pages: 125-146, ISSN: 1991-959X
The interfaces by which users specify the scenarios to be simulated by scientific computer models are frequently primitive, under-documented and ad-hoc text files which make using the model in question difficult and error-prone and significantly increase the development cost of the model. In this paper, we present a model-independent system, Spud, which formalises the specification of model input formats in terms of formal grammars. This is combined with an automated graphical user interface which guides users to create valid model inputs based on the grammar provided, and a generic options reading module which minimises the development cost of adding model options.Together, this provides a user friendly, well documented, self validating user interface which is applicable to a wide range of scientific models and which minimises the developer input required to maintain and extend the model interface.
Farrell PE, Gorman GJ, Piggott MD, et al., 2007, Some problems with the quadratic fitting algorithm for Hessian recovery in the context of anisotropic mesh optimisation, Publisher: CINME, Pages: 101-104-101-104
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