Boundary Element Solver Research Articles

Time-Domain Dynamic Analysis of Helical Gears with Reduced Housing Model

In this paper we present a time-domain dynamic analysis of a helical gear box with different housing models using a unique finite element-contact mechanics solver. The analysis includes detail contact modeling between gear pairs along with the dynamics of gear bodies, shafts, bearings, etc. Inclusion of the housing in the dynamic analysis not only increases the fidelity of the model but also helps estimate important NVH metrics, such as dynamic load and vibration transmission to the base, sound radiation by the gearbox, etc. Two different housing models are considered. In the first, the housing is represented by a full FE mesh, and in the second, the housing is replaced by a reduced model of condensed stiffness and mass matrices. Component Mode Synthesis (CMS) methods are employed to obtain the reduced housing model. Results from both the models are successfully compared to justify the use of reduced housing model for further studies. Steady state sound radiation by the gear box housing is then studied in the frequency domain using a boundary element solver. The housing frequency response, which is the boundary condition for the acoustic analysis, is estimated using two different methods. In one method, the response is computed from the generalized coordinates and component modes using modal superposition, in the other the bearing dynamic loads are used to perform forced response analysis on the full FE mesh of the housing. Thus, a template for end-to-end solution to predict radiated noise from a gear box is established.

Fast multipole accelerated indirect boundary elements for the Helmholtz equation

The indirect boundary element method for the Helmholtz equation in three dimensions is of great interest and practical value for many problems in acoustics as it is capable of treating infinitely thin plates and allows coupling of interior and exterior scattering problems. In the present paper we provide a new approach for treatment of boundary integrals, including hypersingular, singular, and nearly singular integrals via analytical expressions for generic boundary conditions on the both sides of the surface. The fast multipole accelerated boundary element solver in Gumerov and Duraiswami (2009) is extended to incorporate the indirect formulation. The new formulation is compared with the analytical solution of scattering off a disk. Previous authors have not provided such comparisons for an extended range of frequencies. The performance of the method and its scalability are investigated. It is demonstrated that problems with hundreds of thousands of boundary elements can be solved efficiently on a personal computer using the present method.

Electrostatic potentials of proteins in water: a structured continuum approach

Electrostatic interactions play a crucial role in many biomolecular processes, including molecular recognition and binding. Biomolecular electrostatics is modulated to a large extent by the water surrounding the molecules. Here, we present a novel approach to the computation of electrostatic potentials which allows the inclusion of water structure into the classical theory of continuum electrostatics. Based on our recent purely differential formulation of nonlocal electrostatics [Hildebrandt, et al. (2004) Phys. Rev. Lett., 93, 108104] we have developed a new algorithm for its efficient numerical solution. The key component of this algorithm is a boundary element solver, having the same computational complexity as established boundary element methods for local continuum electrostatics. This allows, for the first time, the computation of electrostatic potentials and interactions of large biomolecular systems immersed in water including effects of the solvent's structure in a continuum description. We illustrate the applicability of our approach with two examples, the enzymes trypsin and acetylcholinesterase. The approach is applicable to all problems requiring precise prediction of electrostatic interactions in water, such as protein-ligand and protein-protein docking, folding and chromatin regulation. Initial results indicate that this approach may shed new light on biomolecular electrostatics and on aspects of molecular recognition that classical local electrostatics cannot reveal.

Schematic-Driven Substrate Noise Coupling Analysis in Mixed-Signal IC Designs

This paper presents an approach to reduce substrate cross-talk noise between noisy and sensitive circuitry in mixed-signal integrated circuits at different stages of design and layout development. Silencer! a new, fully automated, schematic-driven substrate noise coupling analysis tool is introduced to accomplish this task. The tool seamlessly enables substrate noise coupling analysis in a standard mixed-signal design flow. Two different methods, fast scalable macro-models and a boundary element solver are integrated into Silencer!. These methods allow extractions of a substrate network from geometric layout information. Simulation results obtained with Silencer! are accurate to within 10% of measured integrated circuits

The design of a boundary element package for treating acoustic scattering from buried objects

The target strength of objects placed in water and partially buried in the sediment are calculated by means of a boundary element solver. For this reason, a boundary element code with suitable pre- and postprocessor is developed. With the help of the preprocessor, the scattering objects within the transition range between fluid and sediment can be modeled. The preprocessor can manage large and complex meshes (more than 100<th>000 elements) and is able to import NASTRAN and ANSYS mesh-files. It automatically generates closed geometric meshes. These meshes are used as database for the BEM calculations. For reducing computing time, the boundary element solver runs on a high number of personal computers in parallel equipped with Windows- or Linux-operating systems. These calculator hosts will receive their task from the preprocessor using TCP/IP-based interprocess communication. The parallel calculations can be performed as a service in the background and remotely administrated by the postprocessor. The postprocessor polls the results from the calculator hosts, delivers them to the appropriate projects, and provides visualization and analysis of the results. The efficiency of such a parallel processing boundary element package will be demonstrated for the acoustic scattering at simple test objects consisting of a high number of surface elements.

Accurate prediction of substrate parasitics in heavily doped CMOS processes using a calibrated boundary element solver

This paper presents an automated methodology for calibrating the doping profile and accurately predicting substrate parasitics with boundary element solvers. The technique requires fabrication of only a few test structures and results in an accurate three-layered approximation of a heavily doped epitaxial silicon substrate. Using this approximation, the extracted substrate resistances are accurate to within 10% of measurements. The calibrated parasitic extractor results in good agreement between simulations and measurements for substrate noise coupling in fabricated test circuits.

A FAST AND STABLE NUMERICAL SOLUTION FOR ACOUSTIC BOUNDARY ELEMENT METHOD EQUATIONS COMBINED WITH THE BURTON AND MILLER METHOD FOR MODELS CONSISTING OF CONSTANT ELEMENTS

Theory and algorithm for the acoustic boundary element solver will be described. The solver represents the core of the package AField (acronym for acoustical field) and can be used for getting fast and stable solutions for huge as well as for small boundary elements models on PCs under Windows. The boundary element solver includes an early proposed GMRES iterative linear system solver (which can be used for big and huge models) and several traditional linear system solvers (for small and medium models). Implementation of the Burthon and Miller regularization method for constant boundary elements will be discussed. Approximations in proposed boundary element solver and their influence on solution errors are investigated. Results for several models are included. Several possibilities of Afield package are illustrated.

An iterative GMRES-based boundary element solver for acoustic scattering

High-frequency scattering of complex structures is studied using a new variant of the generalized minimum residual method (GMRES) along with an appropriate preconditioning, which was originally developed for iterative solutions in electrodynamics [Comparison of GMRES and CG Iterations on the Normal Form of Magnetic Field Integral Equation, submitted]. The starting point is a self-adjoint formulation of the Helmholtz integral equation for scattering. Three iterative methods, the Jacobi iteration with overrelaxation and two variants of the GMRES are presented, and the advantages of the improved GMRES are discussed. The GMRES is applied to the scattering of a plane wave from a cylinder-like, rigid structure comprising several ten thousands of boundary elements. Fast convergence of the iteration process is observed for all investigated cases. The relative error decreases rapidly and becomes smaller than the discretization error after a few iteration steps. The GMRES solver is only weakly affected by internal resonances, but could be combined with a dual-layer CHIEF approach. All computations are carried out on regular personal computers, even for the boundary element model with about 48,000 elements.

Time-domain wave diffraction of two-dimensional single and twin hulls

The nonlinear diffraction of 2D single and twin hulls are studied by employing a mixed Eulerian–Lagrangian model based on a higher-order cubic-spline boundary element solver. Two types of simulations are considered. In the first, waves are generated by a piston-type wave-maker in a rectangular tank and in the second case a nonlinear incident wave is assumed to exist in the tank in which the body is introduced. For the application of this model, the full nonlinear diffraction problem is recast in terms of a perturbation wave-field. Computations are performed for rectangular and triangular hull geometries. Computed results show significant nonlinearities, particularly in the heave force. The twin hull results show the influence of wave interference on the diffraction forces. This interference influences the surge force considerably, but heave force is less affected.

A coupled FE‐BE analysis of acoustic cavities confined inside laminated composite enclosures

The structural acoustic problem, wherein an acoustic domain is confined within a partly flexible laminated composite enclosure is presented. From the finite element free vibration analysis of the laminated folded plate structure a mobility relation is derived between the normal velocity of the structure and normal pressure on the structure. A boundary element solver for the Helmholtz equation with quadratic isoparametric elements is developed using pressure‐velocity formulation. Velocity is known over certain parts of the boundary, the rest being the interactive boundary, where the mobility relation correlates nodal pressures and velocities, neither explicitly known. The pressure boundary values are solved from the boundary element and the mobility relations, while the nodal particle velocities and domain pressures are computed at desired points thereafter. New results presented here reveal the effects of the variation in magnitude of structural damping, fiber angles and the thickness of walls.

Optimization shows Halbach arrays to be non-ideal for induction devices

Among the advantages of Halbach magnet arrays is the fact that the magnetic field behind the array is very small, and the magnets act as a natural flux guide. This paper discusses an optimization index that proves useful for objectively examining any magnet array used in induction applications. Multivariate spline tensor analysis and variable metric methods with a boundary element solver are used to predict the index of performance for these arrays and competing alternatives. The results show that steel based magnet arrays will out-perform conventional Halbach arrays.

Toward functional magnetic stimulation (FMS) theory and experiment.

This paper examines the use of magnetic fields to functionally stimulate peripheral nerves. All electric fields are induced via a changing magnetic field whose flux is entirely confined within a closed magnetic circuit. Induced electric fields are simulated using a nonlinear boundary element solver. The induced fields are solved using duality theory. The accuracy of these predictions is verified by saline bath experiments. Next, the theory is applied to the stimulation of nerves using small, partially occluded ferrite and laminated vanadium permendur cores. Experiments demonstrate the successful stimulation of peripheral nerves in the African bullfrog with 11 mA, 153 mV excitations. These results offer a new vista of possibilities in the area of functional nerve stimulation. Unlike functional electric stimulation (FES), FMS does not involve any half cell reactions, and thus would not have the commensurate FES restrictions regarding balanced biphasic stimulation, strength duration balances, and oxidation issues, always exercising care that the electrodes remain in the reversible operating regime.

High-performance Computers In Advanced Boundary Elements Applications: Non-linear Modelling Of Ship Wave Resistance

The paper presents an algorithm for a non-linear computation of irrotational flow fields with free surface effects. Vectorized and parallelized algorithms and corresponding computer programs are developed for shared and distributed memory computers. Within this context a boundary element solver main tasks are discussed and benchmarked on different platforms. The above formalism is applied to the simulation of a non-linear 3-D numerical towing tank to compute ship wave resistance, wave patterns and fluid flow induced by a steadily advancing ship in calm water.