Gaussian-DPSM (G-DPSM) and Element Source Method (ESM) modifications to DPSM for ultrasonic field modeling

Area of Science:

• Acoustics
• Computational Mechanics
• Numerical Analysis

Background:

• The Distributed Point Source Method (DPSM) is a mesh-free semi-analytical technique for solving field problems.
• A limitation of conventional DPSM is the necessity to scale results to match theoretical solutions.
• Accurate modeling of ultrasonic fields is crucial in various engineering applications.

Purpose of the Study:

• To develop novel modifications of DPSM that obviate the need for scaling.
• To introduce Gaussian-DPSM (G-DPSM) and Element Source Method (ESM) for improved accuracy.
• To validate the performance of G-DPSM and ESM against conventional DPSM and analytical solutions.

Main Methods:

• G-DPSM incorporates additional fictitious child point sources with strengths determined by Gaussian weight functions.
• ESM replaces discrete point sources with continuous sources, forming elements on the boundary.
• Source strength variation within ESM elements can be linear or non-linear based on interpolation functions.

Main Results:

• Both G-DPSM and ESM successfully compute ultrasonic fields without requiring any scaling factor.
• The computed ultrasonic fields closely match theoretical predictions.
• Comparison with conventional DPSM and analytical solutions demonstrates the efficacy of the new methods.

Conclusions:

• G-DPSM and ESM are effective mesh-free techniques for accurate ultrasonic field prediction.
• These methods overcome the scaling limitation of conventional DPSM.
• The developed techniques offer a more direct and accurate approach to modeling transducer fields.