High precision modeling at the 10^{-20} level

The requirements for accurate numerical simulation are increasing constantly. Modern high precision physics experiments now exceed the achievable numerical accuracy of standard commercial and scientific simulation tools. One example are optical resonators for which changes in the optical length are now commonly measured to 10^{-15} precision. The achievable measurement accuracy for resonators and cavities is directly influenced by changes in the distances between the optical components. If deformations in the range of 10^{-15} occur, those effects cannot be modeled and analysed any more with standard methods based on double precision data types. New experimental approaches point out that the achievable experimental accuracies may improve down to the level of 10^{-17} in the near future. For the development and improvement of high precision resonators and the analysis of experimental data, new methods have to be developed which enable the needed level of simulation accuracy. Therefore we plan the development of new high precision algorithms for the simulation and modeling of thermo-mechanical effects with an achievable accuracy of 10^{-20}. In this paper we analyse a test case and identify the problems on the way to this goal.Comment: 7 pages, 10 figure

A new flat shell finite element for the linear analysis of thin shell structures

In this paper, a new rectangular flat shell element denoted ‘ACM_RSBE5’ is presented. The new element is obtained by superposition of the new strain-based membrane element ‘RSBE5’ and the well-known plate bending element ‘ACM’. The element can be used for the analysis of any type of thin shell structures, even if the geometry is irregular. Comparison with other types of shell elements is performed using a series of standard test problems. A correlation study with an experimentally tested aluminium shell is also conducted. The new shell element proved to have a fast rate of convergence and to provide accurate results

Space discontinuous Galerkin method for shallow water flows - kinetic and HLLC flux, and potential vorticity generation

In this paper, a second order space discontinuous Galerkin (DG) method is presented for the numerical solution of inviscid shallow water flows over varying bottom topography. Novel in the implementation is the use of HLLC and kinetic numerical fluxes in combination with a dissipation operator, applied only locally around discontinuities to limit spurious numerical oscillations. Numerical solutions over (non-)uniform meshes are verified against exact solutions; the numerical error in the $L_2$-norm and the convergence of the solution are computed. Bore-vortex interactions are studied analytically and numerically to validate the model; these include bores as "breaking waves'' in a channel and a bore traveling over a conical and Gaussian hump. In these complex numerical test cases, we correctly predict the generation of potential vorticity by non-uniform bores. Finally, we successfully validate the numerical model against measurements of steady oblique hydraulic jumps in a channel with a contraction. In the latter case, the kinetic flux is shown to be more robust

Free vibration analysis of composite right angle triangular plate using a shear flexible element

© 2003 SAGE Publications A high precision triangular plate bending element proposed by the second author of this paper has been upgraded for the free vibration analysis of laminated composite right angle triangular plates. The effect of shear deformation has been incorporated. An efficient mass lumping scheme with rotary inertia has been recommended. Numerical examples of composite triangular plates having different thickness ratios, side ratios, fibre-orientations, number of layers and boundary conditions have been solved by this element. For validation of the present formulation and element few results on isotropic and orthotropic plates have been compared with those obtained from literatures. The results on composite plates have been presented as new results. S. Haldar, D. Sengupta, and A. H. Sheik