A filtered convolution method for the computation of acoustic wave fields in very large spatiotemporal domains

Abstract

The full-wave computation of transient acoustic fields with sizes in the order of 100ϫ 100ϫ 100 wavelengths by 100 periods requires a numerical method that is extremely efficient in terms of storage and computation. Iterative integral equation methods offer a good performance on these points, provided that the recurring spatiotemporal convolutions are computed with a coarse sampling and relatively few computational operations. This paper describes a method for the numerical evaluation of very large-scale, four-dimensional convolutions that employs a fast Fourier transformation and that uses a sampling rate close to or at the limit of two points per wavelength and per period. To achieve this, the functions involved are systematically filtered, windowed, and zero-padded with respect to all relevant coordinates prior to sampling. The method is developed in the context of the Neumann iterative solution of the acoustic contrast source problem for an inhomogeneous medium. The implementation of the method on a parallel computer is discussed. The obtained numerical results have a relative root mean square error of a few percent when sampling at two points per wavelength and per period. Further, the results prove that the method enables the computation of transient fields in the order of the indicated size.

An iterative method for the computation of nonlinear, wide-angle, pulsed acoustic fields of medical diagnostic transducers

“…Such a coarse discretization may be realized with the FC method. 26 In the this section the four steps of the FC method will be briefly summarized, and a specific issue in applying this method to the nonlinear wave problem will be discussed.…”

“…The efficient numerical evaluation of this convolution integral is performed with the Filtered Convolution ͑FC͒ method. This method has been described in more detail in a previous paper 26 that will here be referred to as the FC paper and that will be briefly summarized in this paper. Subsequently, results are presented and discussed for the nonlinear acoustic fields from several types of sources, including medical phased array transducers, and the obtained predictions are compared with results of a number of methods from literature.…”

“…This paper starts with the mathematical formulation of the nonlinear wave propagation problem that results in the lossless Westervelt equation. 25 The nonlinear term in this equation is interpreted as a contrast source, 26 and the nonlinear wave problem is formally solved with an iterative integral equation scheme. The most significant operation in the repeated steps of the iterative scheme is a convolution of Green's function with the primary and contrast sources.…”

Linearization strategies for the Iterative Nonlinear Contrast Source method for full-wave simulation of nonlinear ultrasound fields

“…The most involving task in the numerical evaluation of the scheme is the spatiotemporal convolution, which is ef¿ciently performed with the FFT-based Filtered Convolution method [6].…”

Cumulative phase delay imaging - A new contrast enhanced ultrasound modality

“…In fact, tissue nonlinearity and consequent harmonic formation are a result of the pressure dependency of the speed of sound producing a deformation of the wave-form (wave-form steepening) which cumulates with depth. Figure 1 illustrates this type of deformation by means of numerical results as obtained with the INCS method [4,5]. An example of a transmitted ultrasound gaussian pulse given at the source location (a) and the related deformed pulse after propagation through tissue (b), together with the corresponding frequency spectrum (c) and fundamental and second harmonic time profile (d), are shown.…”