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In some applications, it is reasonable to assume that geodesics (rays) have a consistent orientation so that a time-harmonic elastic wave equation may be viewed as an evolution equation in one of the spatial directions. With such applications in mind, motivated by our recent work [Hadamard- Babich ansatz for point-source elastic wave equations in variable media at high frequencies, Multiscale Model Simul. 19/1 (2021) 46–86], we propose a new truncated Hadamard-Babich ansatz based globally valid asymptotic method, dubbed the fast Huygens sweeping method, for computing Green’s functions of frequency-domain point-source elastic wave equations in inhomogeneous media in the high-frequency asymptotic regime and in the presence of caustics. The first novelty of the fast Huygens sweeping method is that the Huygens-Kirchhoff secondary-source principle is used to integrate many locally valid asymptotic solutions to yield a globally valid asymptotic solution so that caustics can be treated automatically. This yields uniformly accurate solutions both near the source and away from it. The second novelty is that a butterfly algorithm is adapted to accelerate matrix-vector products induced by the Huygens-Kirchhoff integral. The new method enjoys the following desired features: (1) it treats caustics automatically; (2) precomputed asymptotic ingredients can be used to construct Green’s functions of elastic wave equations for many different point sources and for arbitrary frequencies; (3) given a specified number of points per wavelength, it constructs Green’s functions in nearly optimal complexity O(N logN) in terms of the total number of mesh points N, where the prefactor of the complexity depends only on the specified accuracy and is independent of the frequency parameter. Three-dimensional numerical examples are presented to demonstrate the performance and accuracy of the new method.
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HDK: Toward High-Performance Deep-Learning-Based Kirchhoff Analysis
The Kirchhoff law is one of the most widely used physical laws in many engineering principles, e.g., biomedical engineering, electrical engineering, and computer engineering. One challenge of applying the Kirchhoff law to real-world applications at scale lies in the high, if not prohibitive, computational cost to solve a large number of nonlinear equations. Despite recent advances in leveraging a convolutional neural network (CNN) to estimate the solutions of Kirchhoff equations, the low performance is still significantly hindering the broad adoption of CNN-based approaches. This paper proposes a high-performance deep-learning-based approach for Kirchhoff analysis, namely HDK. HDK employs two techniques to improve the performance: (i) early pruning of unqualified input candidates and (ii) parallelization of forward labelling. To retain high accuracy, HDK also applies various optimizations to the data such as randomized augmentation and dimension reduction. Collectively, the aforementioned techniques improve the analysis speed by 8 with accuracy as high as 99.6%.
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- PAR ID:
- 10129635
- Date Published:
- Journal Name:
- Proceedings of the AAAI Conference on Artificial Intelligence
- ISSN:
- 2374-3468
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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