Efficient split eld FDTD analysis of third-order nonlinear materials in two-dimensionally periodic media

In this work the split-field finite-difference time-domain method (SF-FDTD) has been extended for the analysis of two-dimensionally periodic structures with third-order nonlinear media. The accuracy of the method is verified by comparisons with the nonlinear Fourier Modal Method (FMM). Once the formalism has been validated, examples of one- and two-dimensional nonlinear gratings are analysed. Regarding the 2D case, the shifting in resonant waveguides is corroborated. Here, not only the scalar Kerr effect is considered, the tensorial nature of the third-order nonlinear susceptibility is also included. The consideration of nonlinear materials in this kind of devices permits to design tunable devices such as variable band filters. However, the third-order nonlinear susceptibility is usually small and high intensities are needed in order to trigger the nonlinear effect. Here, a one-dimensional CBG is analysed in both linear and nonlinear regime and the shifting of the resonance peaks in both TE and TM are achieved numerically. The application of a numerical method based on the finite- difference time-domain method permits to analyse this issue from the time domain, thus bistability curves are also computed by means of the numerical method. These curves show how the nonlinear effect modifies the properties of the structure as a function of variable input pump field. When taking the nonlinear behaviour into account, the estimation of the electric field components becomes more challenging. In this paper, we present a set of acceleration strategies based on parallel software and hardware solutions.This work was supported by the Ministerio de Economa y Competitividad of Spain under project FIS2014-56100- C2-1-P and by the Generalitat Valenciana of Spain under projects PROMETEOII/2015/015, ISIC/2012/013 and GV/2014/076

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Percussion instrument modelling In 3D: sound synthesis through time domain numerical simulation

This work is concerned with the numerical simulation of percussion instruments based on physical principles. Three novel modular environments for sound synthesis are presented: a system composed of various plates vibrating under nonlinear conditions, a model for a nonlinear double membrane drum and a snare drum. All are embedded in a 3D acoustic environment. The approach adopted is based on the finite difference method, and extends recent results in the field. Starting from simple models, the modular instruments can be created by combining different components in order to obtain virtual environments with increasing complexity. The resulting numerical codes can be used by composers and musicians to create music by specifying the parameters and a score for the systems. Stability is a major concern in numerical simulation. In this work, energy techniques are employed in order to guarantee the stability of the numerical schemes for the virtual instruments, by imposing suitable coupling conditions between the various components of the system. Before presenting the virtual instruments, the various components are individually analysed. Plates are the main elements of the multiple plate system, and they represent the first approximation to the simulation of gongs and cymbals. Similarly to plates, membranes are important in the simulation of drums. Linear and nonlinear plate/membrane vibration is thus the starting point of this work. An important aspect of percussion instruments is the modelling of collisions. A novel approach based on penalty methods is adopted here to describe lumped collisions with a mallet and distributed collisions with a string in the case of a membrane. Another point discussed in the present work is the coupling between 2D structures like plates and membranes with the 3D acoustic field, in order to obtain an integrated system. It is demonstrated how the air coupling can be implemented when nonlinearities and collisions are present. Finally, some attention is devoted to the experimental validation of the numerical simulation in the case of tom tom drums. Preliminary results comparing different types of nonlinear models for membrane vibration are presented

Multi-GPU and multi-CPU accelerated FDTD scheme for vibroacoustic applications

The Finite-Difference Time-Domain (FDTD) method is applied to the analysis of vibroacoustic problems and to study the propagation of longitudinal and transversal waves in a stratified media. The potential of the scheme and the relevance of each acceleration strategy for massively computations in FDTD are demonstrated in this work. In this paper, we propose two new specific implementations of the bi-dimensional scheme of the FDTD method using multi-CPU and multi-GPU, respectively. In the first implementation, an open source message passing interface (OMPI) has been included in order to massively exploit the resources of a biprocessor station with two Intel Xeon processors. Moreover, regarding CPU code version, the streaming SIMD extensions (SSE) and also the advanced vectorial extensions (AVX) have been included with shared memory approaches that take advantage of the multi-core platforms. On the other hand, the second implementation called the multi-GPU code version is based on Peer-to-Peer communications available in CUDA on two GPUs (NVIDIA GTX 670). Subsequently, this paper presents an accurate analysis of the influence of the different code versions including shared memory approaches, vector instructions and multi-processors (both CPU and GPU) and compares them in order to delimit the degree of improvement of using distributed solutions based on multi-CPU and multi-GPU. The performance of both approaches was analysed and it has been demonstrated that the addition of shared memory schemes to CPU computing improves substantially the performance of vector instructions enlarging the simulation sizes that use efficiently the cache memory of CPUs. In this case GPU computing is slightly twice times faster than the fine tuned CPU version in both cases one and two nodes. However, for massively computations explicit vector instructions do not worth it since the memory bandwidth is the limiting factor and the performance tends to be the same than the sequential version with auto-vectorisation and also shared memory approach. In this scenario GPU computing is the best option since it provides a homogeneous behaviour. More specifically, the speedup of GPU computing achieves an upper limit of 12 for both one and two GPUs, whereas the performance reaches peak values of 80 GFlops and 146 GFlops for the performance for one GPU and two GPUs respectively. Finally, the method is applied to an earth crust profile in order to demonstrate the potential of our approach and the necessity of applying acceleration strategies in these type of applications.The work is partially supported by the “Ministerio de Economía y Competitividad” of Spain under project FIS2011-29803-C02-01, by the Spanish Ministry of Education (TIN2012-34557), by the “Generalitat Valenciana” of Spain under projects PROMETEO/2011/021, ISIC/2012/013 and GV/2014/076 and by the “Universidad de Alicante” of Spain under project GRE12-14