1,721,046 research outputs found
Adaptive hp -FEM for eigenvalue computations
Full text linkWe design an adaptive procedure for approximating a selected eigenvalue and its eigen-space for a second-order elliptic boundary-value problem, using an hp finite element method. Such iterative procedure judiciously alternates between a stage in which a near-optimal hp-mesh for the current level of accuracy is generated, and a stage in which such mesh is sufficiently refined to produce a new, enhanced approximation of the eigenfunctions. We identify conditions on the initial mesh and the operator coefficients under which the procedure yields approximations that converge at a geometric rate independent of any discretization parameter, using a number of degrees of freedom comparable to the smallest number needed to get the achieved accuracy. We detail the second stage for a single eigenvalue, relying on a p-robust saturation property
Parallelism in a Highly Accurate Algorithm for Turbulence Simulation
No full textA parallel version of a spectral algorithm for the direct simulation of homogeneous, fully developed turbulence has been developed for the four-processor CRAY X-MP/48. We report a detailed performance analysis which enlights the various factors affecting parallel performance
The shifted boundary method for solid mechanics
No full textWe propose a new embedded/immersed framework for computational solid mechanics, aimed at vastly speeding up the cycle of design and analysis in complex geometry. In many problems of interest, our approach bypasses the complexities associated with the generation of CAD representations and subsequent body-fitted meshing, since it only requires relatively simple representations of the surface geometries to be simulated, such as collections of disconnected triangles in three dimensions, widely used in computer graphics. Our approach avoids the complex treatment of cut elements, by resorting to an approximate boundary representation and a special (shifted) treatment of the boundary conditions to maintain optimal accuracy. Natural applications of the proposed approach are problems in biomechanics and geomechanics, in which the geometry to be simulated is obtained from imaging techniques. Similarly, our computational framework can easily treat geometries that are the result of topology optimization methods and are realized with additive manufacturing technologies. We present a full analysis of stability and convergence of the method, and we complement it with an extensive set of computational experiments in two and three dimensions, for progressively more complex geometries
The second-generation Shifted Boundary Method and its numerical analysis
Full text linkRecently, the Shifted Boundary Method (SBM) was proposed within the class of unfitted (or immersed, or embedded) finite element methods. By reformulating the original boundary value problem over a surrogate (approximate) computational domain, the SBM avoids integration over cut cells and the associated problematic issues regarding numerical stability and matrix conditioning. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions. Hence the name of the method, that shifts the location and values of the boundary conditions. In this article, we present enhanced variational SBM formulations for the Poisson and Stokes problems with improved flexibility and robustness. These simplified variational forms allow to relax some of the assumptions required by the mathematical proofs of stability and convergence of earlier implementations. First, we show that these new SBM implementations can be proved asymptotically stable and convergent even without the rather restrictive assumption that the inner product between the normals to the true and surrogate boundaries is positive. Second, we show that it is not necessary to introduce a stabilization term involving the tangential derivatives of the solution at Dirichlet boundaries, therefore avoiding the calibration of an additional stabilization parameter. Finally, we prove enhanced L2-estimates without the cumbersome assumption – of earlier proofs – that the surrogate domain is convex. Instead we rely on a conventional assumption that the boundary of the true domain is smooth, which can also be replaced by requiring convexity of the true domain. The aforementioned improvements open the way to a more general and efficient implementation of the Shifted Boundary Method, particularly in complex three-dimensional geometries. We complement these theoretical developments with numerical experiments in two and three dimensions
Analysis Of The Shifted Boundary Method For The Poisson Problem In Domains With Corners
No full textThe shifted boundary method (SBM) is an approximate domain method for boundary value problems, in the broader class of unfitted/embedded/immersed methods. It has proven to be quite efficient in handling problems with complex geometries, ranging from Poisson to Darcy, from Navier-Stokes to elasticity and beyond. The key feature of the SBM is a shift in the location where Dirichlet boundary conditions are applied—from the true to a surrogate boundary—and an appropriate modification (again, a shift) of the value of the boundary conditions, in order to reduce the consistency error. In this paper we provide a sound analysis of the method in smooth domains and in domains with corners, highlighting the influence of geometry and distance between exact and surrogate boundaries upon the convergence rate. We consider the Poisson problem with Dirichlet boundary conditions as a model and we first detail a procedure to obtain the crucial shifting between the surrogate and the true boundaries. Next, we give a sufficient condition for the well-posedness and stability of the discrete problem. The behavior of the consistency error arising from shifting the boundary conditions is thoroughly analyzed, for smooth boundaries and for boundaries with corners and edges. The convergence rate is proven to be optimal in the energy norm, and is further enhanced in the L2-norm
Analysis of the shifted boundary method for the Stokes problem
No full textThe analysis of stability and accuracy of the shifted boundary method is developed for the Stokes flow equations. The key feature of the shifted boundary method, an embedded finite element method, is the shifting of the location where boundary conditions are applied from the true to a surrogate boundary, and an appropriate modification (shifting) of the value of the boundary conditions. An inf–sup condition is proved for the variational formulation associated to the shifted boundary method and we derive, by way of Strang's second lemma, an optimal error estimate in the natural SBM norm. We also derive an L2-error estimate for the velocity field, by means of an extension of the Aubin–Nitsche approach to embedded, non-consistent, mixed finite element methods
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Bubble stabilization of spectral Legendre methods for the advection-diffusion equation
No full textCOMPUT. METH. APPL. MECH. ENGN
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