Finite element magnetic field response of an exponential conductivity ground profile

Tunnurak, Priyanuch; Kanyamee, Nairat; Yooyuanyong, Suabsagun

doi:10.12988/ams.2015.52116

Cited by 3 publications

(5 citation statements)

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“…In cylindrical coordinates   z r , , , equation 3can be simplified to be a scalar partial differential equation as [4]…”

Section: Formulation Of the Problemsmentioning

confidence: 99%

“…Finite element method is used to establish a numerical solution of problem. We apply the Galerkin's Method of Weighted Residuals to equation (4). We transform equation 4into weak formulation to find .…”

Section: Formulation Of the Problemsmentioning

confidence: 99%

“…Khonkem and Yooyuanyong [8] also studied magnetic field but the method used is finite different which different from Tunnurak and et al [4].…”

Section: Introductionmentioning

confidence: 98%

“…Both of works done by Chen and Oldenburg [1] and Sripunya and Yooyuanyong [6,7] proposed the Hankel Transforms to solve their problems. Tunnurak and et al [4] used finite element method to study magnetic field on the ground surface. The model, conductivity used, was in the form…”

Section: Introductionmentioning

confidence: 99%

“…The finite element method (FEM) is used to find numerical solutions of magnetic field under the surface of half-space. We assume that the half-space contains only a continuous layer having exponential conductivity bz e   0   which is different from the work done by Tunnurak et al [4]. This method is different from the Hankel transform approach which is used to solve for some specific complex problems such as the research mentioned above by Chen and Oldenburg [1] and Sripunya and Yooyuanyong [6,7].…”

Section: Introductionmentioning

confidence: 99%

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Response of magnetic field from an exponential half-space

Yooyuanyong¹

2017

ams

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We propose mathematical model for magnetic field response from an exponential half-space. The magnetic field at various locations are calculated by assuming that the half-space structure having exponential conductivity profile,. 0 bz e     A Direct Current source and a receiver are provided on the surface of half-space. Finite element method (FEM) is introduced by using the Galerkin's method of Weighted Residuals to find solutions of the Maxwell's equations. Matlab programing is used to calculate and plot graphs of magnetic field intensity at many locations of half-space.

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“…In cylindrical coordinates   z r , , , equation 3can be simplified to be a scalar partial differential equation as [4]…”

Section: Formulation Of the Problemsmentioning

confidence: 99%

Section: Formulation Of the Problemsmentioning

confidence: 99%

“…Khonkem and Yooyuanyong [8] also studied magnetic field but the method used is finite different which different from Tunnurak and et al [4].…”

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Response of magnetic field from an exponential half-space

Yooyuanyong¹

2017

ams

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Fractional Derivatives in Geophysical Modelling: Approaches Using the Modified Adomian Decomposition Method

Prates

Moreira

2020

Pure Appl. Geophys.

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Quantum circuit syntheses of Boolean matrix multiplication using only CNOT gates

Zheng,

Luo,

et al. 2024

Phys. Scr.

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Boolean matrices and operations on Boolean matrices have become increasingly popular in quantum computing and quantum information because they can be used to represent quantum states and the corresponding operations. In this paper, we first give a quantum circuit direct synthesis of general Boolean matrix multiplication using Toffoli gates. We assign a qubit to each element of the matrix and add Toffoli gates at the corresponding positions where the matrix elements are multiplied according to the arithmetic of matrix multiplication. For $n\times p$ dimensional matrix $A$ multiplied by $p\times m$ dimensional matrix $B$, $np + pm + nm$ qubits and at most $pmn$ Toffoli gates are used in total. Then, an improved heuristic algorithm based on matrix Hamming distance selection of CNOT gate is proposed to synthesize the quantum circuit of a matrix, without using wire switching and SWAP gates, using only CNOT gates. The results show that our method is as good as or better than the classical synthesis. Finally, the quantum circuit of Boolean matrix multiplication with at least one invertible or full-rank matrix using only CNOT gates is given, which is divided into five cases for discussion and analysis. For $n\times n$ dimensional invertible matrix $A$ multiplied by $n\times m$ dimensional matrix $B$, $nm$ qubits and at most $mn^{2}$ CNOT gates are used in total. For $n\times p$ dimensional column full-rank matrix $A$ multiplied by $p\times m$ dimensional matrix $B$, $nm$ qubits and at most $pmn$ CNOT gates are used in total. The results show that this method uses less quantum resources to synthesize the quantum circuit of Boolean matrix multiplication. The correctness of the quantum circuits was verified by the Aer simulator of the IBM Quantum platform.

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Finite element magnetic field response of an exponential conductivity ground profile

Cited by 3 publications

References 0 publications

Response of magnetic field from an exponential half-space

Response of magnetic field from an exponential half-space

Fractional Derivatives in Geophysical Modelling: Approaches Using the Modified Adomian Decomposition Method

Quantum circuit syntheses of Boolean matrix multiplication using only CNOT gates

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