Delfim Soares

Explicit time-domain approaches based on numerical Green's functions computed by finite differences - The ExGA family

The present paper describes a new family of time stepping methods to integrate dynamic equations of motion. The scalar wave equation is considered here; however, the method can be applied to time-domain analyses of other hyperbolic (e.g., elastodynamics) or parabolic (e.g., transient diffusion) problems. The algorithms presented require the knowledge of the Greens function of mechanical systems in nodal coordinates. The finite difference method is used here to compute numerically the problem Greens function; however, any other numerical method can be employed, e.g., finite elements, finite volumes, etc. The Greens matrix and its time derivative are computed explicitly through the range [0,@Dt] with either the fourth-order Runge-Kutta algorithm or the central difference scheme. In order to improve the stability of the algorithm based on central differences, an additional matrix called step response is also calculated. The new methods become more stable and accurate when a sub-stepping procedure is adopted to obtain the Greens and step response matrices and their time derivatives at the end of the time step. Three numerical examples are presented to illustrate the high precision of the present approach.

Dynamic analysis of fluid-soil-structure interaction problems by the boundary element method

The present paper describes an iterative procedure for BEM-BEM coupling. The paper presents suitable interface conditions and algorithms for iteratively coupling sub-domains modeled by three different boundary element time-domain formulations, namely: acoustic and elastodynamic BEM formulations based on time-dependent Greens functions and non-linear time-domain approach which employs elastostatic Greens functions and therefore requires domain discretization. Two examples are analyzed and at the end of the paper conclusions of the study are presented.

Time-domain electromagnetic wave propagation analysis by edge-based smoothed point interpolation methods

In this work, smoothed meshfree methods are firstly applied to numerically analyze two-dimensional electromagnetic wave propagation models. A weakened weak formulation based on the edges of triangular cells obtained by a Delaunay triangulation is considered here, framing the so-called edge-based smoothed domains. The meshfree shape functions are computed by the Radial Point Interpolation Method (RPIM) considering two schemes for the shape function support domains, namely the T3- and the T6-scheme. These schemes are based on the above mentioned triangular cells and they consider fixed numbers of nodes for the support domains. A new procedure to compute the transient related matrices is discussed here, aiming to be more consistent with the edge-based smoothed point interpolation method. In this new procedure, finer local integration techniques are managed to be considered at lower computational costs, rendering more accurate and efficient techniques. At the end of the paper, numerical examples are presented, illustrating the effectiveness and potentialities of the proposed methodologies.

An Overview of Recent Advances in the Iterative Analysis of Coupled Models for Wave Propagation

Wave propagation problems can be solved using a variety of methods. However, in many cases, the joint use of different numerical procedures to model different parts of the problem may be advisable and strategies to perform the coupling between them must be developed. Many works have been published on this subject, addressing the case of electromagnetic, acoustic, or elastic waves and making use of different strategies to perform this coupling. Both direct and iterative approaches can be used, and they may exhibit specific advantages and disadvantages. This work focuses on the use of iterative coupling schemes for the analysis of wave propagation problems, presenting an overview of the application of iterative procedures to perform the coupling between different methods. Both frequency- and time-domain analyses are addressed, and problems involving acoustic, mechanical, and electromagnetic wave propagation problems are illustrated.

Axisymmetric Acoustic Modelling by Time-Domain Boundary Element Techniques

In this work, a numerical time-domain approach to model acoustic wave propagation in axisymmetric bodies is developed. The acoustic medium is modeled by the Boundary Element Method (BEM), whose time convolution integrals are evaluated analytically, employing the concept of finite part integrals. All singularities for space integration, present at the expressions generated by time integration, are treated adequately. Some applications are presented in order to demonstrate the validity of the analytical expressions generated for the BEM, and the results obtained with the present approach are compared with those generated by applying numerical time integration.