755 research outputs found

    Inverse problems for linear hyperbolic equations using mixed formulations

    Get PDF
    We introduce in this document a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in Ω×(0,T)\Omega\times (0,T) - Ω\Omega a bounded subset of RN\mathbb{R}^N - from a partial distributed observation. We employ a least-squares technique and minimize the L2L^2-norm of the distance from the observation to any solution. Taking the hyperbolic equation as the main constraint of the problem, the optimality conditions are reduced to a mixed formulation involving both the state to reconstruct and a Lagrange multiplier. Under usual geometric optic conditions, we show the well-posedness of this mixed formulation (in particular the inf-sup condition) and then introduce a numerical approximation based on space-time finite elements discretization. We prove the strong convergence of the approximation and then discussed several examples for N=1N=1 and N=2N=2. The problem of the reconstruction of both the state and the source term is also addressed

    A mixed formulation for the direct approximation of the control of minimal L2L^2-norm for linear type wave equations

    Get PDF
    This paper deals with the numerical computation of null controls for the wave equation with a potential. The goal is to compute approximations of controls that drive the solution from a prescribed initial state to zero at a large enough controllability time. In [\textit{Cindea, Fernandez-Cara \& MĂĽnch, Numerical controllability of the wave equation through primal methods and Carleman estimates, 2013}], a so called primal method is described leading to a strongly convergent approximation of boundary controls : the controls minimize quadratic weighted functionals involving both the control and the state and are obtained by solving the corresponding optimality condition. In this work, we adapt the method to approximate the control of minimal square-integrable norm. The optimality conditions of the problem are reformulated as a mixed formulation involving both the state and his adjoint. We prove the well-posedeness of the mixed formulation (in particular the inf-sup condition) then discuss several numerical experiments. The approach covers both the boundary and the inner controllability. For simplicity, we present the approach in the one dimensional case

    Weather-driven clay cut slope behaviour in a changing climate

    Get PDF
    Long linear earthwork assets constructed in high-plasticity overconsolidated clay are known to be deteriorating due to long-term effects of wetting and drying stress cycles as a result of seasonal weather patterns. These stress cycles can lead to shallow first-time failures due to the mobilisation of post-peak strength and progressive failure. Design requirements of new earthworks and management of existing assets requires improved understanding of this critical mechanism; seasonal ratcheting. Incremental model development and validation to allow investigation of multiple inter-related strength deterioration mechanisms of cut slope behaviour in high-plasticity overconsolidated clay slopes has been presented. Initially, the mechanism of seasonal ratcheting has been considered independently and a numerical modelling approach considering unsaturated behaviour has been validated against physical modelling data. Using the validated model, the effects of slope geometry, design parameter selection and design life have been considered. Following this, an approach to allow undrained unloading of soil, stress relief, excess pore water pressure dissipation, seasonal ratcheting and progressive failure with wetting and drying boundary conditions has been considered. Hydrogeological property deterioration and the potential implications of climate change have been explored using the model. In both cases the serviceable life of cut slopes is shown to reduce significantly in the numerical analyses. Finally, a model capable of capturing hydrogeological behaviour of a real cut slope in London Clay has been developed and validated against long-term field monitored data. Using the validated model, a climate change impact assessment for the case study slope has been performed. The numerical analyses performed have indicated that seasonal ratcheting can explain shallow first-time failures in high-plasticity overconsolidated clay slopes and that the rate of deterioration of such assets will accelerate if current climate change projections are representative of future weather

    The development of virtual leaf surface models for interactive agrichemical spray applications

    Get PDF
    This project constructed virtual plant leaf surfaces from digitised data sets for use in droplet spray models. Digitisation techniques for obtaining data sets for cotton, chenopodium and wheat leaves are discussed and novel algorithms for the reconstruction of the leaves from these three plant species are developed. The reconstructed leaf surfaces are included into agricultural droplet spray models to investigate the effect of the nozzle and spray formulation combination on the proportion of spray retained by the plant. A numerical study of the post-impaction motion of large droplets that have formed on the leaf surface is also considered

    Electromagnetic compatibility and printed circuit boards

    Get PDF

    Structural shape optimization using Cartesian grids and automatic h-adaptive mesh projection

    Full text link
    [EN] We present a novel approach to 3D structural shape optimization that leans on an Immersed Boundary Method. A boundary tracking strategy based on evaluating the intersections between a fixed Cartesian grid and the evolving geometry sorts elements as internal, external and intersected. The integration procedure used by the NURBS-Enhanced Finite Element Method accurately accounts for the nonconformity between the fixed embedding discretization and the evolving structural shape, avoiding the creation of a boundary-fitted mesh for each design iteration, yielding in very efficient mesh generation process. A Cartesian hierarchical data structure improves the efficiency of the analyzes, allowing for trivial data sharing between similar entities or for an optimal reordering of thematrices for the solution of the system of equations, among other benefits. Shape optimization requires the sufficiently accurate structural analysis of a large number of different designs, presenting the computational cost for each design as a critical issue. The information required to create 3D Cartesian h- adapted mesh for new geometries is projected from previously analyzed geometries using shape sensitivity results. Then, the refinement criterion permits one to directly build h-adapted mesh on the new designs with a specified and controlled error level. Several examples are presented to show how the techniques here proposed considerably improve the computational efficiency of the optimization process.The authors wish to thank the Spanish Ministerio de Economia y Competitividad for the financial support received through the project DPI2013-46317-R and the FPI program (BES-2011-044080), and the Generalitat Valenciana through the project PROMETEO/2016/007.Marco, O.; Ródenas, J.; Albelda Vitoria, J.; Nadal, E.; Tur Valiente, M. (2017). Structural shape optimization using Cartesian grids and automatic h-adaptive mesh projection. Structural and Multidisciplinary Optimization. 1-21. https://doi.org/10.1007/s00158-017-1875-1S121MATLAB version 8.3.0.532 (R2014a) (2014) Documentation. The Mathworks, Inc., Natick, MassachusettsAbel JF, Shephard MS (1979) An algorithm for multipoint constraints in finite element analysis. Int J Numer Methods Eng 14(3):464–467Amestoy P, Davis T, Duff I (1996) An approximate minimum degree ordering algorithm. SIAM J Matrix Anal Appl 17(4):886–905Barth W, Stürzlinger W (1993) Efficient ray tracing for Bezier and B-spline surfaces. Comput Graph 17 (4):423–430Bennett J A, Botkin M E (1985) Structural shape optimization with geometric problem description and adaptive mesh refinement. AIAA J 23(3):459–464Braibant V, Fleury C (1984) Shape optimal design using b-splines. Comput Methods Appl Mech Eng 44 (3):247–267Bugeda G, Oliver J (1993) A general methodology for structural shape optimization problems using automatic adaptive remeshing. Int J Numer Methods Eng 36(18):3161–3185Bugeda G, Ródenas J J, Oñate E (2008) An integration of a low cost adaptive remeshing strategy in the solution of structural shape optimization problems using evolutionary methods. Comput Struct 86(13–14):1563–1578Chang K, Choi K K (1992) A geometry-based parameterization method for shape design of elastic solids. Mech Struct Mach 20(2):215–252Cho S, Ha S H (2009) Isogeometric shape design optimization: exact geometry and enhanced sensitivity. Struct Multidiscip Optim 38(1):53–70Belegundu D, Zhang YMS, Salagame R (1991) The natural approach for shape optimization with mesh distortion control. Tech. rep., Penn State UniversityDavis T A, Gilbert J R, Larimore S, Ng E (2004) An approximate column minimum degree ordering algorithm. ACM Trans Math Softw 30(3):353–376Doctor L J, Torborg J G (1981) Display techniques for octree-encoded objects. IEEE Comput Graph Appl 1(3):29–38Dunning P D, Kim H A, Mullineux G (2011) Investigation and improvement of sensitivity computation using the area-fraction weighted fixed grid FEM and structural optimization. Finite Elem Anal Des 47(8):933–941Düster A, Parvizian J, Yang Z, Rank E (2008) The finite cell method for three-dimensional problems of solid mechanics. Comput Methods Appl Mech Eng 197(45-48):3768–3782Escobar J M, Montenegro R, Rodríguez E, Cascón J M (2014) The meccano method for isogeometric solid modeling and applications. Eng Comput 30(3):331–343Farhat C, Lacour C, Rixen D (1998) Incorporation of linear multipoint constraints in substructure based iterative solvers. Part 1: a numerically scalable algorithm. Int J Numer Methods Eng 43(6):997–1016Fries T P, Omerović S (2016) Higher-order accurate integration of implicit geometries. Int J Numer Methods Eng 106(5):323–371Fuenmayor F J, Oliver J L (1996) Criteria to achieve nearly optimal meshes in the h-adaptive finite element mehod. Int J Numer Methods Eng 39(23):4039–4061Fuenmayor F J, Oliver J L, Ródenas J J (1997) Extension of the Zienkiewicz-Zhu error estimator to shape sensitivity analysis. Int J Numer Methods Eng 40(8):1413–1433García-Ruíz M J, Steven G P (1999) Fixed grid finite elements in elasticity problems. Eng Comput 16 (2):145–164Gill P, Murray W, Saunders M, Wright M (1984) Procedures for optimization problems with a mixture of bounds and general linear constraints. ACM Trans Math Software 10:282–298González-Estrada O A, Nadal E, Ródenas J J, Kerfriden P, Bordas S P A, Fuenmayor F J (2014) Mesh adaptivity driven by goal-oriented locally equilibrated superconvergent patch recovery. Comput Mech 53(5):957–976Ha S H, Choi K K, Cho S (2010) Numerical method for shape optimization using T-spline based isogeometric method. Struct Multidiscip Optim 42(3):417–428Haftka R T, Grandhi R V (1986) Structural shape optimization: A survey. Comput Methods Appl Mech Eng 57(1):91–106Haslinger J, Jedelsky D (1996) Genetic algorithms and fictitious domain based approaches in shape optimization. Struc Optim 12:257–264Hughes T J R, Cottrell J A, Bazilevs Y (2005) Isogeometric Analysis: CAD, Finite Elements, NURBS, Exact Geometry, and Mesh Refinement. Comput Methods Appl Mech Eng 194:4135–4195Jackins C L, Tanimoto S L (1980) Oct-tree and their use in representing three-dimensional objects. Comput Graphics Image Process 14(3):249–270Kajiya J T (1982) Ray Tracing Parametric Patches. SIGGRAPH Comput Graph 16(3):245–254van Keulen F, Haftka R T, Kim N (2005) Review of options for structural design sensitivity analysis. Part I: linear systems. Comput Methods Appl Mech Eng 194(30-33):3213–3243Kibsgaard S (1992) Sensitivity analysis-the basis for optimization. Int J Numer Methods Eng 34(3):901–932Kikuchi N, Chung K Y, Torigaki T, Taylor J E (1986) Adaptive finite element methods for shape optimization of linearly elastic structures. Comput Methods Appl Mech Eng 57(1):67–89Kim N H, Chang Y (2005) Eulerian shape design sensitivity analysis and optimization with a fixed grid. Comput Methods Appl Mech Eng 194(30–33):3291–3314Kudela L, Zander N, Kollmannsberger S, Rank E (2016) Smart octrees: Accurately integrating discontinuous functions in 3d. Comput Methods Appl Mech Eng 306(1):406–426Kunisch K, Peichl G (1996) Numerical gradients for shape optimization based on embedding domain techniques. Comput Optim 18:95–114Li K, Qian X (2011) Isogeometric analysis and shape optimization via boundary integral. Computer-Aided Design 43(11):1427–1437Lian H, Kerfriden P, Bordas S P A (2016) Implementation of regularized isogeometric boundary element methods for gradient-based shape optimization in two-dimensional linear elasticity. Int J Numer Methods Eng 106 (12):972–1017Liu L, Zhang Y, Hughes T J R, Scott M A, Sederberg T W (2014) Volumetric T-spline Construction using Boolean Operations. Eng Comput 30(4):425–439Marco O, Sevilla R, Zhang Y, Ródenas J J, Tur M (2015) Exact 3D boundary representation in finite element analysis based on Cartesian grids independent of the geometry. Int J Numer Methods Eng 103:445–468Marco O, Ródenas J J, Fuenmayor FJ, Tur M (2017a) An extension of shape sensitivity analysis to an immersed boundary method based on cartesian grids. Computational Mechanics SubmittedMarco O, Ródenas J J, Navarro-Jiménez JM, Tur M (2017b) Robust h-adaptive meshing strategy for arbitrary cad geometries in a cartesian grid framework. Computers & Structures SubmittedMeagher D (1980) Octree Encoding: A New Technique for the Representation, Manipulation and Display of Arbitrary 3-D Objects by Computer. Tech. Rep. IPL-TR-80-11 I, Rensselaer Polytechnic InstituteMoita J S, Infante J, Mota C M, Mota C A (2000) Sensitivity analysis and optimal design of geometrically non-linear laminated plates and shells. Comput Struct 76(1–3):407–420Nadal E (2014) Cartesian Grid FEM (cgFEM): High Performance h-adaptive FE Analysis with Efficient Error Control. Application to Structural Shape Optimization. PhD Thesis. Universitat Politècnica de ValènciaNadal E, Ródenas J J, Albelda J, Tur M, Tarancón J E, Fuenmayor F J (2013) Efficient finite element methodology based on cartesian grids: application to structural shape optimization. Abstr Appl Anal 2013:1–19Najafi A R, Safdari M, Tortorelli D A, Geubelle P H (2015) A gradient-based shape optimization scheme using an interface-enriched generalized FEM. Comput Methods Appl Mech Eng 296:1–17Nguyen V P, Anitescu C, Bordas S P A, Rabczuk T (2015) Isogeometric analysis: An overview and computer implementation aspects. Math Comput Simul 117:89–116Nishita T, Sederberg TW, Kakimoto M (1990) Ray Tracing Trimmed Rational Surface Patches. SIGGRAPH Comput Graph 24(4):337–345Nocedal J, Wright SJ (2006) Numerical optimization, 2nd edn. Springer-Verlag, New YorkPandey P C, Bakshi P (1999) Analytical response sensitivity computation using hybrid finite elements. Comput Struct 71(5):525–534Parvizian J, Düster A, Rank E (2007) Finite Cell Method: h- and p- Extension for Embedded Domain Methods in Solid Mechanics. Comput Mech 41(1):121–133Peskin C S (1977) Numerical Analysis of Blood Flow in the Heart. J Comput Phys 25:220–252Poldneff M J, Rai I S, Arora J S (1993) Implementation of design sensitivity analysis for nonlinear structures. AIAA J 31(11):2137–2142Powell M (1983) Variable metric methods for constrained optimization. In: Bachem A, Grotschel M, Korte B (eds) Mathematical Programming: The State of the Art, Springer, Berlin, Heidelberg, pp 288–311Qian X (2010) Full analytical sensitivities in NURBS based isogeometric shape optimization. Comput Methods Appl Mech Eng 199(29–32):2059–2071Riehl S, Steinmann P (2014) An integrated approach to shape optimization and mesh adaptivity based on material residual forces. Comput Methods Appl Mech Eng 278:640–663Riehl S, Steinmann P (2016) On structural shape optimization using an embedding domain discretization technique. Int J Numer Methods Eng 109(9):1315–1343Ródenas J J, Tarancón J E, Albelda J, Roda A, Fuenmayor F J (2005) Hierarchical Properties in Elements Obtained by Subdivision: a Hierarquical h-adaptivity Program. In: Díez P, Wiberg N E (eds) Adaptive Modeling and Simulation, p 2005Ródenas J J, Corral C, Albelda J, Mas J, Adam C (2007a) Nested domain decomposition direct and iterative solvers based on a hierarchical h-adaptive finite element code. In: Runesson K, Díez P (eds) Adaptive Modeling and Simulation 2007, Internacional Center for Numerical Methods in Engineering (CIMNE), pp 206–209Ródenas J J, Tur M, Fuenmayor F J, Vercher A (2007b) Improvement of the superconvergent patch recovery technique by the use of constraint equations: the SPR-C technique. Int J Numer Methods Eng 70(6):705–727Ródenas J J, Bugeda G, Albelda J, Oñate E (2011) On the need for the use of error-controlled finite element analyses in structural shape optimization processes. Int J Numer Methods Eng 87(11):1105–1126Schillinger D, Ruess M (2015) The finite cell method: A review in the context of higher-order structural analysis of cad and image-based geometric models. Arch Comput Meth Eng 22(3):391– 455Sevilla R, Fernández-Méndez S, Huerta A (2011a) 3D-NURBS-enhanced Finite Element Method (NEFEM). Int J Numer Methods Eng 88(2):103–125Sevilla R, Fernández-Méndez S, Huerta A (2011b) Comparison of High-order Curved Finite Elements. Int J Numer Methods Eng 87(8):719–734Sevilla R, Fernández-Méndez S, Huerta A (2011c) NURBS-enhanced Finite Element Method (NEFEM): A Seamless Bridge Between CAD and FEM. Arch Comput Meth Eng 18(4):441–484Sweeney M, Bartels R (1986) Ray tracing free-form b-spline surfaces. IEEE Comput Graph Appl 6(2):41–49Toth D L (1985) On Ray Tracing Parametric Surfaces. SIGGRAPH Comput Graph 19(3):171–179Tur M, Albelda J, Nadal E, Ródenas J J (2014) Imposing dirichlet boundary conditions in hierarchical cartesian meshes by means of stabilized lagrange multipliers. Int J Numer Methods Eng 98(6):399–417Tur M, Albelda J, Marco O, Ródenas J J (2015) Stabilized Method to Impose Dirichlet Boundary Conditions using a Smooth Stress Field. Comput Methods Appl Mech Eng 296:352–375Yao T, Choi KK (1989) 3-d shape optimal design and automatic finite element regridding. Int J Numer Methods Eng 28(2):369–384Zhang L, Gerstenberger A, Wang X, Liu W K (2004) Immersed Finite Element Method. Comput Methods Appl Mech Eng 293(21):2051–2067Zhang Y, Wang W, Hughes T J R (2013) Conformal Solid T-spline Construction from Boundary T-spline Representations. Comput Mech 6(51):1051–1059Zienkiewicz O C, Zhu J Z (1987) A Simple Error Estimator and Adaptive Procedure for Practical Engineering Analysis. Int J Numer Methods Eng 24(2):337–35

    Computer-aided modeling for efficient and innovative product-process engineering

    Get PDF
    Model baserede computer understøttet produkt process engineering har opnået øget betydning i forskelligste industrielle brancher som for eksampel farmaceutisk produktion, petrokemi, finkemikalier, polymerer, bioteknologi, fødevarer, energi og vand. Denne trend er forventet at fortsætte på grund af substantielle fordele, hvilke computer understøttede metoder medfører. Den primære forudsætning af computer understøttet produkt process engineering erselvfølgelig den tilgængelighed af modeller af forskellige typer, former og anvendelser. Udviklingen af den påkrævet modellen for de undersøgte systemer er normalt en tidskrævende udfordring og derfor mest også dyrt. Den involverer forskelligste trin, fagekspert viden og dygtighed og forskellige modellerings værktøjer. Formålet af dette projekt er at systematisere den model udviklings proces og anvendelse og dermed øge effektiviteten af modeller såvel somkvaliteten. Den væsentlige bidrag af denne PhD afhandling er en generisk metodologi for proces model udviklingen og anvendelse i kombination med grundige algoritmiske arbejdes diagrammer for de forskellige involverede modeller opgaver og udviklingen af computer understøttede modeller rammer hvilke er strukturbaseret på den generiske metodologi, delvis automatiseret i de forskellige arbejdstrin og kombinerer alle påkrævet værktøjer, understøttelseog vejledning for de forskellige arbejdstrin. Understøttede modelleringsopgaver er etableringen af modeller mål, indsamling af de nødvendige informationer, model formulering inklusive numeriske analyser, etablering af løsningsstrategier og forbinding med den passende løsningsmodul, model identificering og sondering såvel som model anvendelse for simulation og optimering. Den computer understøttede modeller ramme blev implementeret i en brugervenlig software. En række forskellige demonstrationseksempler fra forskellige områder i kemisk ogbiokemiske engineering blev løst for udvikling og validering af den generiske modellerings metodologi og den computer understøttet modeller ramme anvendt på den udviklet software værktøj.Model-based computer aided product-process engineering has attained increased importance in a number of industries, including pharmaceuticals, petrochemicals, fine chemicals, polymers, biotechnology, food, energy and water. This trend is set to continue due to the substantial benefits computer-aided methods provide. The key prerequisite of computer-aided productprocess engineering is however the availability of models of different types, forms andapplication modes. The development of the models required for the systems under investigation tends to be a challenging, time-consuming and therefore cost-intensive task involving numerous steps, expert skills and different modelling tools. The objective of this project is to systematize the process of model development and application thereby increasing the efficiency of the modeller as well as model quality.The main contributions of this thesis are a generic methodology for the process of model development and application, combining in-depth algorithmic work-flows for the different modelling tasks involved and the development of a computer-aided modelling framework. This framework is structured, is based on the generic modelling methodology, partially automates the involved work-flows by integrating the required tools and, supports and guides the userthrough the different work-flow steps. Supported modelling tasks are the establishment of the modelling objective, the collection of the required system information, model construction including numerical analysis, derivation of solution strategy and connection to appropriate solvers, model identification/ discrimination as well as model application for simulation and optimization. The computer-aided modelling framework has been implemented into an userfriendlysoftware.A variety of case studies from different areas in chemical and biochemical engineering have been solved to illustrate the application of the generic modelling methodology, the computeraided modelling framework and the developed software tool
    • …
    corecore