Helmholtz-Kirchhoff Integral Near-Field Singularity Handling
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Solution Overview
Problem
Existing methods for calculating the Helmholtz-Kirchhoff integral, particularly in the context of Numerical Acoustics, face challenges with near-field singularities, leading to inaccurate acoustic results close to the object's surface, which is critical for industrial applications.
Innovation Solution
The proposed method identifies near-field singularity field points and applies a local projection to determine an associated model mesh element. It then calculates the Helmholtz-Kirchhoff integral using an adaptive quadrature order based on the ratio of minimum normal distance to element size, and employs a coordinate transformation to improve accuracy and efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If the Helmholtz-Kirchhoff integral is calculated using standard methods, then the calculation can be performed efficiently, but the accuracy deteriorates for field points close to the object's surface due to near-field singularities
Solution Approach 1:
The patent applies different calculation strategies to different regions: standard integration for far-field points and singularity-handling integration for near-field points. This local differentiation allows efficient calculation where possible while maintaining accuracy where needed, resolving the contradiction between overall efficiency and local precision.
Solution Approach 2:
The patent segments the field points into two categories: those close to the surface (requiring special handling) and those farther away (using standard methods). This segmentation allows the system to apply appropriate methods to each group, maintaining both efficiency and accuracy.
2Measurement precision
If the number of quadrature points is increased to improve accuracy near the surface, then the measurement precision improves, but the computational time increases significantly
Solution Approach 1:
The patent dynamically changes the quadrature order parameter based on the distance ratio. For near-field points, it uses higher quadrature orders (5-10) to achieve accuracy, while for far-field points, it uses lower orders (2-4) to save time. This adaptive parameter adjustment resolves the contradiction between precision and computational cost.
Solution Approach 2:
The patent makes the integration parameters dynamic rather than static. The quadrature order and integration strategy are adjusted in real-time based on the calculated distance ratio between field points and surface elements, allowing the system to optimize between accuracy and speed for each specific case.
3Measurement precision
If a coordinate transformation is applied to handle near-field singularities, then the accuracy for near-field points improves, but the device complexity increases
Solution Approach 1:
The patent introduces an intermediary classification system that identifies near-field points and routes them to specialized integration methods. This intermediary layer (the distance ratio calculation and point classification mechanism) manages the complexity by automatically selecting appropriate methods, making the overall system easier to implement than manual complex integration for all points.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach effectively handles near-field singularities, providing accurate acoustic results even for field points close to the object's surface, thus enhancing the computational efficiency and accuracy for industrial-scale problems.
Implementation Method 1
post-processing the result by assigning to said field points at least one parameter determined from calculating the Helmholtz-Kirchhoff integral from said result
Data Source
AI summary
Method of determining acoustic parameters of an object's (OBJ) emission and/or scattering, in particular for improving acoustic properties of said object (OBJ), comprising: (a) defining a model (MDL) including said object (OBJ), a sound source (SCR), and a surrounding area, (b) processing said model (MDL) obtaining a result (RST), (c) post-processing the result (RST) by assigning to said field points (PTS) at least one parameter (PRM) determined from calculating the Helmholtz-Kirchhoff integral from said result (RST). To improve the accuracy and efficiency the post-processing comprises the additional steps: (d) identifying field points (PTS) as near field singularity field points (NEP) of potential lower result (RST) accuracy (ACR), (c) determining for said near field singularity field points (NEP) respectively an associated model mesh element (AME), by determining a local projection from said near field singularity field point (NEP) to the object's (OBJ) surface by calculating a minimum normal distance (MND) to the object's (OBJ) surface, wherein the associated model mesh element (AME) being the touchdown point of the local projection, (f) determining for said near field singularity field points (NEP) respectively a ratio (RTO) of the minimum normal distance (MND) to said element size (ESZ) of the associated model mesh element (AME), (g) calculating the Helmholtz-Kirchhoff integral by: (g11) providing a relation (PCR) of quadrature order (QOD) and said ratio (RTO), (g2) determine the respective quadrature order (QOD) by applying said relation (PCR), (g3) calculating the Helmholtz-Kirchhoff integral from said result (RST).