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• Computational strategies for the solution of large nonlinear problems via quasi-newton methods

  M. Geradin, S. Idelsohn, M. Hogge

  Computers and Structures (1981). Vol. 13 (1-3), pp. 73-81

  
  

  Abstract

  The usefulness of quasi-Newton methods for the solution of nonlinear systems of equations is demonstrated. After a review of the Newton iterative method, several quasi-Newton updates are presented and tested. Special attention is devoted to the solution of large sparse systems of equations such as those issued from spatial discretization of continua by finite elements. The numerical examples presented comprise static and dynamic analyses of geometrical, material and combined nonlinear structural problems and a model fluid flow problem with different levels of nonlinearity. All the results are assorted with a complete discussion of the different methods used, of the convergence rates and of the associated computer costs. From the present studies, it can be concluded that computational costs for the solution of large nonlinear systems of equations can be reduced drastically by using convenient quasi-Newton updates or by adequate combined Newton/quasi-Newton strategies.

  Abstract
  The usefulness of quasi-Newton methods for the solution of nonlinear systems of equations is demonstrated. After a review of the Newton iterative method, several quasi-Newton [...]

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• Failure internal pressure of spherical steel containments

  G. Sarmiento, S. Idelsohn, A. Cardona, V. Sonzogni

  Nuclear Engineering and Desing (1985). Vol. 90 (2), pp. 209-222

  
  

  Abstract

  An application of the British CEGB's R6 Failure Assessment Approach to the determination of failure internal pressure of nuclear power plant spherical steel containments is presented. The presence of hypothetical cracks both in the base metal and in the welding material of the containment, with geometrical idealizations according to the ASME Boiler and Pressure Vessel Code (Section XI), was taken into account in order to analyze the sensitivity of the failure assessment with the values of the material fracture properties. Calculations of the elastoplastic collapse load have been performed by means of the Finite Element System SAMCEF. The clean axisymmetric shell (neglecting the influence of nozzles and minor irregularities) and two major penetrations (personnel and emergency locks) have been taken separately into account. Large-strain elastoplastic behaviour of the material was considered in the Code, using lower bounds of true stress—true strain relations obtained by testing a collection of tensile specimens. Assuming the presence of cracks in non-perturbed regions, the reserve factor for test pressure and the failure internal pressure have been determined as a function of the flaw depth.

  Abstract
  An application of the British CEGB's R6 Failure Assessment Approach to the determination of failure internal pressure of nuclear power plant spherical steel containments [...]

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• Nonlinear structural dynamics via Newton and quasi-Newton methods

  M. Geradin, S. Idelsohn, M. Hogge

  Nuclear Engineering and Design (1980). Vol. 58 (3), pp. 339-348;

  
  

  Abstract

  This paper is an attempt to compare Newton and quasi-Newton methods in nonlinear structural dynamics. After a review of the classical iterative methods, several quasi-Newton updates are presented and tested. Special attention is devoted to the solution of large sparse systems for which two original procedures are described: a substructure correction and a vectorial correction. The numerical examples presented include the dynamic analyses of geometrical, material and combined nonlinearities. All the results are assorted with a complete discussion of the different methods used, of the convergence rates and of the associated computer costs. From the present results, Newton's methods appear to exhibit the best convergence rates when an efficient computational strategy is adopted. Nevertheless computational costs for the solution of large systems can be reduced drastically by using convenient quasi-Newton updates.

  Abstract
  This paper is an attempt to compare Newton and quasi-Newton methods in nonlinear structural dynamics. After a review of the classical iterative methods, several quasi-Newton [...]

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

  F. Mossaiby, R. Rossi, P. Dadvand, S. Idelsohn

  Int. J. Numer. Meth. Engng. (2012). Vol. 89 (13), pp. 1635-1651

  
  

  Abstract

  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.

  Abstract
  The solution of problems in computational fluid dynamics (CFD) represents a classical field for the application of advanced numerical methods. Many different approaches were [...]

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• All‐hexahedral element meshing: automatic elimination of self‐intersecting dual lines

  N. Calvo, S. Idelsohn

  Int. J. Numer. Meth. Engng. (2002). Vol. 55 (12), pp. 1439-1449

  
  

  Abstract

  There has been some degree of success in all‐hexahedral meshing. Standard methods start with the object geometry defined by means of an all‐quadrilateral mesh, followed by the use of the combinatorial dual to the mesh in order to define the internal connectivities among elements. For all of the known methods using the dual concept, it is necessary to first prevent or eliminate self‐intersecting (SI) dual lines of the given quadrilateral mesh. The relevant features of SI lines are studied, giving a method to remove them, which avoids deforming the original geometry. Some examples of resulting meshes are shown where the current meshing method has been successfully applied. 

  Abstract
  There has been some degree of success in all‐hexahedral meshing. Standard methods start with the object geometry defined by means of an all‐quadrilateral mesh, followed [...]

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• All‐hexahedral mesh smoothing with a node‐based measure of quality

  N. Calvo, S. Idelsohn

  Int. J. Numer. Meth. Engng. (2001). Vol. 50 (8), pp. 1957-1967

  
  

  Abstract

  This research work deals with the analysis and test of a normalized‐Jacobian metric used as a measure of the quality of all‐hexahedral meshes. Instead of element qualities, a measure of node quality was chosen. The chosen metric is a bound for deviation from orthogonality of faces and dihedral angles. We outline the main steps and algorithms of a program that is successful in improving the quality of initially invalid meshes to acceptable levels. For node movements, the program relies on a combination of gradient‐driven and simulated annealing techniques. Some examples of the results and speed are also shown.

  Abstract
  This research work deals with the analysis and test of a normalized‐Jacobian metric used as a measure of the quality of all‐hexahedral meshes. Instead of element qualities, [...]

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• Non‐reflective planar boundary condition based on Gauss filter

  R. Bonet Chaple, N. Nigro, M. Storti, S. Idelsohn

  Int. J. Numer. Meth. Engng. (2000). Vol. 47 (5), pp. 969-983

  
  

  Abstract

  A non‐reflecting boundary condition based on the Gauss filter is employed for the determination of scattered potential governed by the equation. A filtering layer is used for closing infinite domain calculations. An expression for the reflection coefficient is derived and an optimal filtering layer is designed. Numerical results validate the performance of this method for unbounded wave guide problems.

  Abstract
  A non‐reflecting boundary condition based on the Gauss filter is employed for the determination of scattered potential governed by the equation. A filtering layer is used [...]

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• A finite point method in computational mechancis. Applications to convective transport and fluid flow.

  E. Oñate, S. Idelsohn, O. Zienkiewicz, R. Taylor

  Int. J. Numer. Meth. Engng. (1996). Vol. 39 (22), pp. 3839-3866

  
  

  Abstract

  The paper presents a fully meshless procedure fo solving partial differential equations. The approach termed generically the ‘finite point method’ is based on a weighted least square interpolation of point data and point collocation for evaluating the approximation integrals. Some examples showing the accuracy of the method for solution of adjoint and non‐self adjoint equations typical of convective‐diffusive transport and also to the analysis of compressible fluid mechanics problem are presented.

  Abstract
  The paper presents a fully meshless procedure fo solving partial differential equations. The approach termed generically the ‘finite point method’ is based on [...]

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• Transient analysis of tube rolling processes by a semi‐analytical formulation

  H. Antúnez, S. Idelsohn

  Int. J. Numer. Meth. Engng. (1994). Vol. 37 (21), pp. 3621-3632

  
  

  Abstract

  A semi‐analytical formulation is presented for transient metal‐forming processes which, being axisymmetric in geometry, are subjected to non‐axisymmetric loads and boundary conditions. The problems are described in terms of the flow formulation, and the pseudo‐concentration method (two material based) is used to account for time integration and non‐axisymmetric free surfaces. Proper Fourier series expansion of both the scalar fields defined to identify the free surfaces and of all the variables of the mechanical problem allows the performance of an advective transport–corresponding to time integration–for a non‐axisymmetric velocity field. A block diagonal matrix is obtained for each harmonic component, as it has been achieved for the constant time solution. The new configuration found as a result of this analysis is taken to calculate the velocity field for the incremented time, which in turn is used to perform the following time step

  Abstract
  A semi‐analytical formulation is presented for transient metal‐forming processes which, being axisymmetric in geometry, are subjected to non‐axisymmetric loads and boundary [...]

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• A preconditioning mass matrix to accelerate the convergence to the steady Euler solutions using explicit schemes

  M. Storti, C. Baumann, S. Idelsohn

  Int. J. Numer. Meth. Engng. (1992). Vol. 34 (2), pp. 519-541

  
  

  Abstract

  When explicit time marching algorithms are used to reach the steady state of problems governed by the Euler equations, the rate of convergence is strongly impaired both in the zones with low Mach number and in the zones with transonic flow, e.g. Mach ⩽ α and | Mach − 1| ⩽ α, with α ⩽ 0·2. The rate of convergence becomes slower as α diminishes. We show in this paper, with analytical and numerical results, how the use of a preconditioning mass matrix accelerates the convergence in the aforementioned ranges of Mach numbers. The preconditioning mass matrix (PMM) we advocate in this paper can be applied to any FEM/FVM that uses an explicit time marching scheme to find the steady state. The method's rate of convergence to the steady state is studied, and results for the one‐ and two‐dimiensional cases are presented. In Sections 1‐3, using the one‐dimensional Euler equations, we first explain why there exists a slow rate of convergence when the plain lumping of mass is used. Then the convergence rate to steady solutions is analysed from its two constituents, that is, convergence by absorption at the boundaries and by damping in the domain. Next we give the natural solution to this problem, and with several examples we show the effectiveness of the proposed mass matrix when compared with the plain scheme. In Sections 4‐8 we give the multidimensional version of the preconditioning mass matrix. We make a stability analysis and compare the group velocities and damping with and without the new mass matrix. To finish, we show the velocity of convergence for a common test problem

  Abstract
  When explicit time marching algorithms are used to reach the steady state of problems governed by the Euler equations, the rate of convergence is strongly impaired both in [...]

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