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  • 1
    Electronic Resource
    Electronic Resource
    Conjugate direction methods for helmholtz problems with complex-valued wavenumbers (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 601-622 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The convergence behaviour of conjugate direction methods for Helmholtz problems with complex-valued wavenumbers is studied. The model problem is a Galerkin discretization of the scalar Helmholtz equation on square arrays of 2D and 3D, C° linear elements. A series of controlled experiments is performed which use the dimensionless wavenumber and the algebraic size of the system of equations to completely characterize the iterative performance of the solvers. The effects of algebraic size are examined as functions of both mesh refinement and mesh extension within the limits of present-day workstation computing environments. A comparison is drawn between the conjugate direction methods investigated and the equivalent time-domain solution obtained through explicit time-stepping.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620350311
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Three-dimensional hydrodynamics on finite elements. Part II: Non-linear time-stepping model (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 12 (1991), S. 507-533 
    Details
    ISSN: 0271-2091
    Keywords: Finite elements ; Hydrodynamics ; Three-dimensional hydrodynamics ; Non-linear hydrodynamics ; Tidal hydrodynamics ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The development and application of a non-linear 3D hydrodynamic model are described. The model is based on the wave equation rearrangement of the primitive 3D shallow water equations with a general eddy viscosity formulation for the vertical shear. A Galerkin procedure is used to discretize these on simple sixnode elements: linear triangles in the horizontal with linear variations in the vertical. Resolution of surface, bottom and interfacial boundary layers is facilitated and total flexibility is preserved for specifying spatial and temporal variations in the vertical viscosity and density fields. A semi-implicit time-stepping algorithm allows the solutions for elevation and velocity to be uncoupled during each time step. The elevation solution is essentially a 2D wave equation calculation with a stationary sparse matrix representing the gravity waves. With nodal quadrature the subsequent velocity calculation is achieved by factoring only a tridiagonal diffusion matrix representing the vertical viscous terms. As a result the overall calculation scales computationally as only a 2D problem but provides the full 3D solution. Application to field-scale problems is illustrated for the English Channel/Southern Bight system and the Lake Maracaibo system.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650120602
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A second-order radiation boundary condition for the shallow water wave equations on two-dimensional unstructured finite element grids (1994)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 575-604 
    Details
    ISSN: 0271-2091
    Keywords: Radiation boundary conditions ; Open boundary conditions ; Shallow water wave equations ; Sommerfeld condition ; Klein-Gordon equation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A second-order radiation boundary condition (RBC) is derived for 2D shallow water problems posed in ‘wave equation’ form and is implemented within the Galerkin finite element framework. The RBC is derived by matching the dispersion relation for the interior wave equation with an approximate solution to the exterior problem for outgoing waves. The matching is correct to second order, accounting for curvature of the wave front and the geometry. Implementation is achieved by using the RBC as an evolution equation for the normal gradient on the boundary, coupled through the natural boundary integral of the Galerkin interior problem. The formulation is easily implemented on non-straight, unstructured meshes of simple elements. Test cases show fidelity to solutions obtained on extended meshes and improvement relative to simpler first-order RBCs.
    Additional Material: 28 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650180604
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    Paper (German National Licenses)
    Fulltext
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