Fourier Transformation method for solving integral equation in the 2.5D problem of electric sounding

Rakisheva, D.S.; Mukanova, Balgaisha

doi:10.1088/1742-6596/2092/1/012018

Cited by 2 publications

(4 citation statements)

References 9 publications

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“…in the analysis of the next stage. One method used to determine the frequency of a signal is to use the Fourier Transformation Method (FFT) (Rakisheva & Mukanova, 2021;Setiawan, 2022). Fourier transforms aims to convert time-time sound signals into the frequency domain (Apoorva, 2021;Zhang & Ma, 2022).…”

Section: Discussionmentioning

confidence: 99%

Gamelan Data Repository: The Implementation of Information and Communication Technology Preserving the Balinese Traditional Musical Orchestra

Dantes

2022

j. sains. teknologi.

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As the knowledge to build Balinese orchestra are passed down from generation to another within the clan, the orchestras across makers and across areas in Bali show subtle but distinctive differences in their tones, which may be altered when the knowledge is passed down manually. Research aimed at digitalizing these distinct differences in the creations of the Balinese Orchestra across craftsmen clans in Bali is conducted as an effort for preserving the unique differences produced by the respective clans through the development of a system prototype and database for storing the tones in the orchestra sets. The steps design to attain these purposes comprised of (1) analyzing the needs of preserving the Balinese Orchestra and mapping the problems faced by traditional craftsmen in maintaining standard tones; (2) designing a system to record the standard tones among craftsmen in Bali, i.e. sampling two most two groups of craftsmen from two regencies recognized as having the most distinctive tones in Bali, namely South of Bali and North of Bali; (3) developing the prototype; and (4) developing the database of Balinese Orchestra. When the database is ready, it will provide a reference for craftsmen to standardize their sets according to the intended tradition while opening a wide possibility of uses ranging from evaluation to the creation of collaborative musical compositions across media, while at the same time preserving the standardized tone in digitalized storage.

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Section: Discussionmentioning

confidence: 99%

Gamelan Data Repository: The Implementation of Information and Communication Technology Preserving the Balinese Traditional Musical Orchestra

Dantes

2022

j. sains. teknologi.

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“…As shown in Figure 1, point E corresponds to boundary between the dam, water, and air. Numerical simulations of the electrical field and apparent resistivities, as described in (Rakisheva and Mukanova, 2021, [11]) and (Rakisheva et al, 2020, [12]), illustrate significant anomalies of the electric field in the proximity of this boundary. Consequently, refining the grid near this point is desirable.…”

Section: Mathematical Model and Adaptive Triangulation Of Surfacesmentioning

confidence: 99%

“…For instance, in the article (Turarova et al, 2022, [10]), explicit computations elucidate the influence of the three-dimensional medium structure on 2D inversion results. The papers (Rakisheva, Mukanova, 2021, [11]) and (Rakisheva et al, 2021, [12]) show numerically how relief features affect sounding curves. In the monograph (Mukanova, Modin, 2018, [13]), various examples of ERT method simulations are presented via the formulation of integral equations.…”

Section: Introductionmentioning

confidence: 99%

“…The article (Turarova et al, 2022, [14]) is dedicated to explicitly calculating sounding curves in the presence of surface relief and developing a method to filter out nonphysical anomalies from interpretation results. Generally speaking, articles [10] and [11] emphasize the advantages of the integral equation method compared to techniques that necessitate the discretization of the entire three-dimensional domain, a common approach in the mathematical modeling of 3D problems. Applications of the finite element method and integral equations to problems in electrodynamics are also discussed in the monographs [14] (Shi-zhe Xu, 2001) and [15] (Zhdanov, 2015).…”

Section: Introductionmentioning

confidence: 99%

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Simplified Adaptive Triangulation of the Contact Boundaries of the Dam Model

Mukanova

2023

sjaitu

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To numerically solve the system of integral equations, it is customary to establish a discrete grid within each integration area. In the context of 3D modeling, these areas correspond to surfaces situated in space. The standard discretization technique employed for the computational domain is triangulation. This study addresses the integral equation system pertinent to the electrical tomography of dams. The structural model encompasses an embankment dam, the upstream and downstream water bodies, the dam's base, and a potential leakage region on the upstream side. An alternative configuration may be encountered in specific scenarios with no water downstream. Consequently, the model may incorporate up to nine distinct contact boundaries. Accordingly, the system of integral equations comprises an equivalent number of equations. Effectively resolving this system through numerical methods necessitates applying triangulation techniques to these diverse surfaces. While mathematical packages like Matlab offer triangulation functions, they may not fully address the specific demands of the problem. Additionally, the grid resolution should be heightened in proximity to key elements such as the sounding line, the supply electrode, and the various contact lines within the medium. These considerations transform the triangulation task into a distinct subtask within the numerical simulation of the resistivity tomography problem. In this paper, we provide our specific approach to this problem. The simplification of the triangulation algorithm is rooted in the predominant utilization of the two-dimensional geometric properties inherent to the object under study. For most contact boundaries, the triangulation is constructed layer by layer with a gradual modulation in triangle dimensions as one progresses from one layer to the next, orthogonal to the axis of the dam. Concerning the surface corresponding to the leakage area, cylindrical coordinates are used for surface parameterization. This approach enables partitioning the surface into discrete strata, facilitating a systematic, layer-by-layer grid construction. Additionally, points at the intersections of contact boundaries are integrated into the pre-existing triangulation by applying a standard function within the Matlab package. In the future, the mathematical modeling based on the Integral Equation Method with adaptive discretization will help incorporate real-time computations into information systems related to monitoring hydraulic structures.

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Fourier Transformation method for solving integral equation in the 2.5D problem of electric sounding

Cited by 2 publications

References 9 publications

Gamelan Data Repository: The Implementation of Information and Communication Technology Preserving the Balinese Traditional Musical Orchestra

Gamelan Data Repository: The Implementation of Information and Communication Technology Preserving the Balinese Traditional Musical Orchestra

Simplified Adaptive Triangulation of the Contact Boundaries of the Dam Model

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