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Christian Michler - One of the best experts on this subject based on the ideXlab platform.
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An investigation of Interface-GMRES(R) for fluid–structure interaction problems with flutter and divergence
Computational Mechanics, 2011Co-Authors: Christian Michler, Harald Brummelen, Rene De BorstAbstract:The basic Subiteration method for solving fluid–structure interaction problems consists of an iterative process in which the fluid and structure subsystems are alternatingly solved, subject to complementary partitions of the interface conditions. The main advantages of the Subiteration method are its conceptual simplicity and its modularity. The method has several deficiencies, however, including a lack of robustness and efficiency. To bypass these deficiencies while retaining the main advantages of the method, we recently proposed the Interface-GMRES(R) solution method, which is based on the combination of Subiteration with a Newton–Krylov approach, in which the Krylov space is restricted to the interface degrees-of-freedom. In the present work, we investigate the properties of the Interface-GMRES(R) method for two distinct fluid–structure interaction problems with parameter-dependent stability behaviour, viz., the beam problem and the string problem. The results demonstrate the efficiency and robustness of the Interface-GMRES(R) method.
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VALIDATION OF THE INTERFACE-GMRES(R) SOLUTION METHOD FOR FLUID-STRUCTURE INTERACTIONS
2006Co-Authors: Christian Michler, Van Eh Harald Brummelen, R In 't Groen, De R René BorstAbstract:The numerical solution of fluid-structure interactions with the customary Subiteration method incurs numerous deficiencies. We validate a recently proposed solution method based on the conjugation of Subiteration with a Newton-Krylov method, and demonstrate its superiority and beneficial characteristics.
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VALIDATION OF THE INTERFACE-GMRES(R) SOLUTION METHOD FOR FLUID-STRUCTURE INTERACTIONS
2006Co-Authors: P. Wesseling, Christian Michler, Harald Van Brummeleny, Rob In&aposAbstract:reuse of Krylov vectors Abstract. The numerical solution of uid-structure interactions with the customary Subiteration method incurs numerous deciencies. We validate a recently proposed solu-tion method based on the conjugation of Subiteration with a Newton-Krylov method, and demonstrate its superiority and benecial characteristics.
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Error-amplification analysis of Subiteration-preconditioned GMRES for fluid-structure interaction
Computer Methods in Applied Mechanics and Engineering, 2005Co-Authors: Christian Michler, Van Eh Harald Brummelen, De R René BorstAbstract:The customary Subiteration method for solving fluid–structure-interaction problems exhibits several deficiencies, viz., only conditional stability, potential convergence difficulties due to non-normality-induced divergence, and the inability to reuse information from previously solved similar problems. To overcome these deficiencies, a novel solution method is considered, in which Subiteration is used as a preconditioner to GMRES. This paper treats the linear-algebra aspects of the Subiteration method, and of the Subiteration-preconditioned GMRES method, on the basis of properties of the error-amplification matrix for the aggregated fluid–structure system. An analysis of the error-amplification matrix of Subiteration establishes that Subiteration condenses errors into a low-dimensional subspace which can be associated with the interface degrees-of-freedom. Therefore, the GMRES acceleration of Subiteration can be confined to the interface degrees-of-freedom. The error-amplification analysis provides a clear explanation of the relation between the local GMRES acceleration (i.e., on the interface degrees-of-freedom), and the global error-amplification properties (i.e., for the aggregated system). Moreover, we show that the Subiteration iterates span a Krylov space corresponding to a preconditioned aggregated system. We then address the implications of the non-normality of the Subiteration preconditioner for the convergence of GMRES. The Subiteration-preconditioned GMRES method enables the optional reuse of Krylov vectors in subsequent invocations of GMRES, which can substantially enhance the efficiency of the method. To assess the potential and the limitations of the reuse option, we analyse the error-amplification matrix of the GMRES method with reuse. Furthermore, we establish that the GMRES acceleration on the interface degrees-of-freedom generates an approximation to the Schur complement for the aggregated system. The GMRES acceleration and the reuse of Krylov vectors are then assessed in terms of the approximation properties for the Schur complement, and in terms of the properties of the corresponding error-amplification matrices. Numerical experiments on a model fluid–structure-interaction problem illustrate the developed theory. In particular, we analyse the convergence of the respective methods in terms of spectral radii, matrix norms and sharp convergence upper bounds.
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Efficient Numerical Methods for Fluid-Structure Interaction
2005Co-Authors: Christian MichlerAbstract:Numerical solution methods for fluid-structure interaction are of great importance in many engineering disciplines. The computation of fluid-structure interactions is challenging on account of their free-boundary and multi-physics character. The different length and time scale discretization requirements of the fluid and structure subsystems typically translate into the use of non-matching meshes at the fluid-structure interface. Under such an incompatible discretization, maintaining the conservation properties at the fluid-structure interface is in general non-trivial. Moreover, the solution of the coupled fluid-structure equations by the customary Subiteration method often lacks robustness and efficiency. These aspects provide the motivation for the research into conservative discretization techniques and efficient iterative solution methods for fluid-structure interaction presented in this thesis. We investigate an approach that enables conservation at the interface even for incompatible fluid and structure discretizations. Numerical results demonstrate the relevance of maintaining conservation at the fluid-structure interface for the stability and accuracy of the numerical solution. To overcome the deficiencies of the Subiteration solution method, we propose to combine Subiteration with GMRES acceleration. Since the acceleration can be confined to the degrees-of-freedom of the interface, the acceleration itself requires only negligible computational resources. Moreover, the combined method allows for the optional reuse of Krylov vectors in subsequent invocations of GMRES, which can considerably enhance the efficiency of the method. Since the proposed method retains the modularity of the underlying Subiteration method, its implementation is straightforward in codes that already use Subiteration as a solver. Detailed convergence studies and a comparison with standard Subiteration demonstrate the effectiveness of the proposed solution method.
Kalman Palagyi - One of the best experts on this subject based on the ideXlab platform.
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equivalent sequential and parallel Subiteration based surface thinning algorithms
International Workshop on Combinatorial Image Analysis, 2015Co-Authors: Kalman Palagyi, Gábor Németh, Péter KardosAbstract:Thinning is a frequently applied technique for extracting skeletons or medial surfaces from volumetric binary objects. It is an iterative object reduction: border points that satisfy certaini¾?topological and geometric constraints are deleted in a thinning phase. Sequential thinning algorithms may alter just one point at a time, while parallel algorithms can delete a set of border points simultaneously. Two thinning algorithms are said to be equivalent if they can produce the same result for each input binary picture. This work shows that it is possible to construct Subiteration-based equivalent sequential and parallel surface-thinning algorithms. The proposed four pairs of algorithms can be implemented directly on a conventional sequential computer or on a parallel computing device. All of them preserve topology for 26,i¾?6 pictures.
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Topology-preserving equivalent parallel and sequential 4-Subiteration 2D thinning algorithms
2015 9th International Symposium on Image and Signal Processing and Analysis (ISPA), 2015Co-Authors: Kalman Palagyi, Gábor Németh, Péter KardosAbstract:Thinning is a frequently applied technique for extracting centerlines from 2D binary objects. Parallel thinning algorithms can remove a set of object points simultaneously, while sequential algorithms traverse the boundary of objects, and consider the actually visited single point for possible removal. Two thinning algorithms are called equivalent if they produce the same result for each input picture. This paper presents the very first pair of equivalent 2D sequential and parallel Subiteration-based thinning algorithms. These algorithms can be implemented directly on a conventional sequential computer or on a parallel computing device. Both of them preserve topology for (8, 4) pictures sampled on the square grid.
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parallel 3d 12 Subiteration thinning algorithms based on isthmuses
International Symposium on Visual Computing, 2013Co-Authors: Kalman PalagyiAbstract:Thinning is an iterative object reduction to obtain skeleton-like shape features of volumetric binary objects. Conventional thinning algorithms preserve endpoints to provide important geometric information relative to the object to be represented. An alternative strategy is also proposed that accumulates isthmuses i.e., generalization of curve and surface interior points as skeletal elements. This paper presents two parallel isthmus-based 3D thinning algorithms that are capable of producing centerlines and medial surfaces. The strategy which is used is called Subiteration-based or directional: each iteration step is composed of 12 Subiterations each of which are executed in parallel. The proposed algorithms make efficient implementation possible and their topological correctness is guaranteed.
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A 3–Subiteration Surface–Thinning Algorithm
2011Co-Authors: Kalman PalagyiAbstract:Abstract. Thinning is an iterative layer by layer erosion for extracting skeleton. This paper presents an efficient parallel 3D thinning algorithm which produces medial surfaces. A three–Subiteration strategy is proposed: the thinning operation is changed from iteration to iteration with a period of three according to the three deletion directions.
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a family of topology preserving 3d parallel 6 Subiteration thinning algorithms
International Workshop on Combinatorial Image Analysis, 2011Co-Authors: Gábor Németh, Péter Kardos, Kalman PalagyiAbstract:Thinning is an iterative layer-by-layer erosion until only the skeleton-like shape features of the objects are left. This paper presents a family of new 3D parallel thinning algorithms that are based on our new sufficient conditions for 3D parallel reduction operators to preserve topology. The strategy which is used is called Subiteration-based: each iteration step is composed of six parallel reduction operators according to the six main directions in 3D. The major contributions of this paper are: 1) Some new sufficient conditions for topology preserving parallel reductions are introduced. 2) A new 6-Subiteration thinning scheme is proposed. Its topological correctness is guaranteed, since its deletion rules are derived from our sufficient conditions for topology preservation. 3) The proposed thinning scheme with different characterizations of endpoints yields various new algorithms for extracting centerlines and medial surfaces from 3D binary pictures.
E. H. Van Brummelen - One of the best experts on this subject based on the ideXlab platform.
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Added mass effects of compressible and incompressible flows in fluid–structure interaction
2020Co-Authors: E. H. Van BrummelenAbstract:The Subiteration method, which forms the basic iterative procedure for solving fluidstructure-interactio
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FLUID-STRUCTURE-INTERACTION PROBLEM∗
2016Co-Authors: E. H. Van Brummelen, R. De BorstAbstract:Abstract. Subiteration forms the basic iterative method for solving the aggregated equations in fluid-structure-interaction problems, in which the fluid and structure equations are solved alter-natingly subject to complementary partitions of the interface conditions. In the present work we establish for a prototypical model problem that the Subiteration method can be characterized by re-cursion of a nonnormal operator. This implies that the method typically converges nonmonotonously. Despite formal stability, divergence can occur before asymptotic convergence sets in. It is shown that the transient divergence can amplify the initial error by many orders of magnitude, thus inducing a severe degradation in the robustness and efficiency of the Subiteration method. Auxiliary results concern the dependence of the stability and convergence of the Subiteration method on the physical parameters in the problem and on the computational time step
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Added Mass Effects of Compressible and Incompressible Flows in Fluid-Structure Interaction
Journal of Applied Mechanics, 2009Co-Authors: E. H. Van BrummelenAbstract:The Subiteration method, which forms the basic iterative procedure for solving fluid- structure-interaction problems, is based on a partitioning of the fluid-structure system into a fluidic part and a structural part. In fluid-structure interaction, on short time scales the fluid appears as an added mass to the structural operator, and the stability and convergence properties of the Subiteration process depend significantly on the ratio of this apparent added mass to the actual structural mass. In the present paper, we establish that the added-mass effects corresponding to compressible and incompressible flows are fundamentally different. For a model problem, we show that on increasingly small time intervals, the added mass of a compressible flow is proportional to the length of the time interval, whereas the added mass of an incompressible flow approaches a constant. We then consider the implications of this difference in proportionality for the stability and convergence properties of the Subiteration process, and for the stability and accuracy of loosely coupled staggered time-integration methods.
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A Space-Time Finite Element Approach to the Numerical Simulation of Vascular Fluid-Solid Interaction
2008Co-Authors: E.j. Vlijm, E. H. Van BrummelenAbstract:Numerical studies of cardiovascular diseases like arteriosclerosis have gained increasing attention the last decade. The modeling of blood, blood vessel and their coupling, shows to be a challenging problem. In this thesis a two-dimensional model has been constructed and its behaviour has been investigated. We model the blood vessel by a linear elastic continuum and blood by an incompressible Newtonian fluid. The coupled system is solved with a space-time discontinuous Galerkin method. The solution is allowed to be discontinuous over the discrete time level, but continuity in space is enforced. We calculate the movement of the fluid domain by the equations of linear elasticity, which results in a so-called ’pseudo solid’ mapping. The coupled system is solved with a strongly-coupled solution method. The Subiteration procedure occurring within each time step is accelerated by relaxation. Relaxation shows to be necessary when the density of the structure approaches the density of the fluid. The number of iteration steps needed within a time step shows to be quite large and the need for better acceleration becomes apparent. Although the relaxation technique offers some improvement of the Subiteration procedure, better techniques are necessary for three-dimensional simulations.
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on the nonnormality of Subiteration for a fluid structure interaction problem
SIAM Journal on Scientific Computing, 2005Co-Authors: E. H. Van Brummelen, R. De BorstAbstract:Subiteration forms the basic iterative method for solving the aggregated equations in fluid-structure-interaction problems, in which the fluid and structure equations are solved alternatingly subject to complementary partitions of the interface conditions. In the present work we establish for a prototypical model problem that the Subiteration method can be characterized by recursion of a nonnormal operator. This implies that the method typically converges nonmonotonously. Despite formal stability, divergence can occur before asymptotic convergence sets in. It is shown that the transient divergence can amplify the initial error by many orders of magnitude, thus inducing a severe degradation in the robustness and efficiency of the Subiteration method. Auxiliary results concern the dependence of the stability and convergence of the Subiteration method on the physical parameters in the problem and on the computational time step.
Rene De Borst - One of the best experts on this subject based on the ideXlab platform.
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An investigation of Interface-GMRES(R) for fluid–structure interaction problems with flutter and divergence
Computational Mechanics, 2011Co-Authors: Christian Michler, Harald Brummelen, Rene De BorstAbstract:The basic Subiteration method for solving fluid–structure interaction problems consists of an iterative process in which the fluid and structure subsystems are alternatingly solved, subject to complementary partitions of the interface conditions. The main advantages of the Subiteration method are its conceptual simplicity and its modularity. The method has several deficiencies, however, including a lack of robustness and efficiency. To bypass these deficiencies while retaining the main advantages of the method, we recently proposed the Interface-GMRES(R) solution method, which is based on the combination of Subiteration with a Newton–Krylov approach, in which the Krylov space is restricted to the interface degrees-of-freedom. In the present work, we investigate the properties of the Interface-GMRES(R) method for two distinct fluid–structure interaction problems with parameter-dependent stability behaviour, viz., the beam problem and the string problem. The results demonstrate the efficiency and robustness of the Interface-GMRES(R) method.
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An interface Newton-Krylov solver for fluid-structure interaction
International Journal for Numerical Methods in Fluids, 2005Co-Authors: Christian Michler, E. H. Van Brummelen, Rene De BorstAbstract:The numerical solution of fluid-structure interactions with the customary Subiteration method incurs numerous deficiencies. We propose a novel solution method based on the conjugation of Subiteration with a Newton-Krylov method, and demonstrate its superiority and beneficial characteristics.
H Bijl - One of the best experts on this subject based on the ideXlab platform.
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analysis and application of high order implicit runge kutta schemes for unsteady conjugate heat transfer a strongly coupled approach
Journal of Computational Physics, 2014Co-Authors: V Kazemikamyab, A H Van Zuijlen, H BijlAbstract:Abstract Thermal interaction of fluids and solids, or conjugate heat transfer (CHT), is encountered in many engineering applications. Since time-accurate computations of unsteady CHT can be computationally demanding, we consider the use of high order implicit time integration schemes which have the potential to be more efficient relative to the commonly used second order implicit schemes. We present a strongly-coupled solution algorithm where the high order L-stable explicit first-stage singly diagonally implicit Runge–Kutta (ESDIRK) schemes are used to advance the solution in time within each separate fluid and solid subdomains. Furthermore, the stability and rate of convergence of performing (Gauss–Seidel) Subiterations at each stage of the ESDIRK schemes are analyzed. The results from solving a numerical example (an unsteady conjugate natural convection in an enclosure) show good agreement with the performed analytical stability analysis. In addition, the (computational) work-(temporal) precision character of several schemes in solving a strongly coupled CHT problem is compared over a range of accuracy requirements. From the efficiency investigation, it is observed that performing Subiterations with the strongly-coupled ESDIRK algorithm is more efficient than lowering time-step size using a high order loosely-coupled IMEX algorithm. In addition, by using the ESDIRK schemes, gain in computational efficiency relative to Crank–Nicolson is observed for time-accurate solutions (a factor of 1.4 using the fourth order ESDIRK). The computational gain is higher for smaller tolerances.
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Multi-level and quasi-Newton acceleration for strongly coupled partitioned fluid-structure interaction
2011Co-Authors: Jasper Kreeft, A H Van Zuijlen, M. Weghs, H BijlAbstract:Two reduced order models are presented for the simulation of physically strong coupled fluid-structure interaction problem, based on computationally partitioned flow and structure solvers. The reduced order models used are a class of quasi-Newton coupling methods to obtain a stable solution and to reduce the number of Subiterations. The second reduced order model is a multi-level acceleration in with coarse grid computations are performed in order to reduce computational costs. Finally an adaptive multi-level strategy is described, that contains an indicator for when to switch from coarse to fine grid level and vice versa.
