A general algorithm for accurate computation of field variables and its derivatives near the boundary in BEM

Ma, Hang; Kamiya, N.

doi:10.1016/s0955-7997(01)00073-x

Cited by 34 publications

(29 citation statements)

References 4 publications

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“…Suppose that B * (ξ) is the fundamental solution or its derivative, while F S (ξ) denotes the corresponding asymptotic function, i.e., Eqs. (15), (16) or (17). In this case the general form of the boundary integral over Γ Shell, j can be rearranged as where G 0 and φ 0 are the values of G(ξ) and φ(ξ) at the position ξ = ξ 0 on the boundary element that is the nearest to the location of the magnetic sensor i under consideration.…”

Section: Accurate Computation Of Boundary Integrals Along the Shellmentioning

confidence: 99%

“…The total integrand of the first integral has no singularity and can therefore be evaluated with the ordinary Gaussian quadrature [12] with 16 integration points for each boundary element. Ma and Kamiya [16] proposed the use of an approximated 'distance function' for the boundary element adjacent to the sensor position (a, b) as…”

Section: Accurate Computation Of Boundary Integrals Along the Shellmentioning

confidence: 99%

“…This distance function agrees with ε in Eqs. (15), (16) and (17) when ξ → ξ 0 and d 0 → 0. If one defines the (r, z) coordinates corresponding to ξ = −1, 0 and 1 on the quadratic boundary element as (r 1 , z 1 ), (r 2 , z 2 ) and (r 3 , z 3 ), the coordinate at an arbitrary point on the element can be given by…”

Section: Accurate Computation Of Boundary Integrals Along the Shellmentioning

confidence: 99%

See 2 more Smart Citations

Reconstruction of the Eddy Current Distribution on the Vacuum Vessel in a Reversed Field Pinch Device based on the External Magnetic Sensor Signals

Itagaki

Sanpei

Masamune

et al. 2014

Plasma and Fusion Research

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For the MHD equilibrium reconstruction of a reverse field pinch device, it is a big issue to identify accurately the strong eddy current flow on the shell. In the present work, boundary integrals of the eddy current along the shell are added to the conventional Cauchy-condition surface method formulation. The eddy current profile is unknown in advance but straightforwardly identified using only the signals from magnetic sensors located outside the plasma. Two ideas are introduced to overcome the numerical difficulties encountered in the problem. One is an accurate boundary integral scheme to damp out the near singularity occurring at the sensor position very close to the shell. The other is the modified truncated singular value decomposition technique to solve an illconditioned matrix equation when a large number of nodal points exist on the shell. The capability of the new method is demonstrated for a test problem modeling the RELAX device.

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Section: Accurate Computation Of Boundary Integrals Along the Shellmentioning

confidence: 99%

Section: Accurate Computation Of Boundary Integrals Along the Shellmentioning

confidence: 99%

Section: Accurate Computation Of Boundary Integrals Along the Shellmentioning

confidence: 99%

See 1 more Smart Citation

Reconstruction of the Eddy Current Distribution on the Vacuum Vessel in a Reversed Field Pinch Device based on the External Magnetic Sensor Signals

Itagaki

Sanpei

Masamune

et al. 2014

Plasma and Fusion Research

View full text Add to dashboard Cite

show abstract

“…The total integrand of the first integral has no singularity and can therefore be evaluated with the ordinary Gaussian quadrature with 16 integration points for each boundary element. Ma and Kamiya [6] proposed the use of an approximated 'distance function' for the boundary element adjacent to the sensor position (a, b) as …”

Section: Accurate Computation Of Boundary Integrals Along the Shellmentioning

confidence: 99%

Reconstruction of the eddy current profile on the vacuum vessel in a nuclear fusion device using only external magnetic sensor signals

Itagaki¹,

Sanpei²,

Masamune³

et al. 2014

WIT Transactions on Modelling and Simulation

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In a reversed field pinch device, the ordinary Cauchy-condition surface (CCS) method cannot reconstruct the magnetic flux profile accurately due to the strong eddy current flow on the shell (vacuum vessel). Boundary integrals of the eddy current density along the shell are added to the original CCS method formulation. The eddy current profile is unknown in advance but identified using only the signals of magnetic sensors located outside the plasma. As the sensors are closely adjacent to the shell, the near singular boundary integrals along the shell should be accurately evaluated. This singularity can be damped out with the algorithm based on the distance function proposed by Ma and Kamiya. The modified truncated singular value decomposition technique of Hansen et al. is an effective way to solve an ill-conditioned matrix equation when a large number of nodal points exist on the shell. The capability of the new method is demonstrated for a test problem modelling the RELAX device.

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“…The importance of this subject area is considered second only to the singular case of the boundary element method and this explains the great attention and effort that has been focused on it in recent years [11][12][13][14][15][16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

A general algorithm for the numerical evaluation of nearly singular boundary integrals of various orders for two- and three-dimensional elasticity

Ma¹,

Kamiya

2002

Computational Mechanics

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A general algorithm of the distance transformation type is presented in this paper for the accurate numerical evaluation of nearly singular boundary integrals encountered in elasticity, which, next to the singular ones, has long been an issue of major concern in computational mechanics with boundary element methods. The distance transformation is realized by making use of the distance functions, defined in the local intrinsic coordinate systems, which plays the role of damping-out the near singularity of integrands resulting from the very small distance between the source and the integration points. By taking advantage of the divergence-free property of the integrals with the nearly hypersingular kernels in the 3D case, a technique of geometric conversion over the auxiliary cone surfaces of the boundary element is designed, which is suitable also for the numerical evaluation of the hypersingular boundary integrals. The effects of the distance transformations are studied and compared numerically for different orders in the 2D case and in the different local systems in the 3D case using quadratic boundary elements. It is shown that the proposed algorithm works very well, by using standard Gaussian quadrature formulae, for both the 2D and 3D elastic problems. IntroductionThe accurate numerical evaluation of nearly singular boundary integrals has challenged researchers since the advent of the boundary element method. The problem generally refers to the boundary layer effect, a phenomenon that the boundary integrals cannot be computed accurately with the ordinary Gaussian quadrature if the computing point is located closely adjacent to the boundary [1-3]. Similar to the case of singular boundary integrals, the boundary layer effect comes from the properties of fundamental solutions and their derivatives, having the denominator of the Euclidean distance, r, between the source and the field points of various orders [4]. In consequence, the values of the integrals over a boundary element have a reverse correlation with this distance relative to the size of the element, so the system matrices are well behaved so enabling the boundary integrals to be evaluated accurately.The accurate numerical evaluation of nearly singular boundary integrals is crucial for many engineering problems, including, for example, the analysis of the thin or shell-like bodies as occur in many structural applications [5][6][7], the crack problems when the crack tip is deformed with an opening displacement [8], the contact problem [9] when the distance between the two contacting bodies is very small, as well as the sensitivity problem [10]. The importance of this subject area is considered second only to the singular case of the boundary element method and this explains the great attention and effort that has been focused on it in recent years [11][12][13][14][15][16][17][18][19][20][21][22][23].The difficulty encountered in the numerical evaluation results mainly from the fact that the integrands of nearly singular boundary integrals vary drastical...

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A general algorithm for accurate computation of field variables and its derivatives near the boundary in BEM

Cited by 34 publications

References 4 publications

Reconstruction of the Eddy Current Distribution on the Vacuum Vessel in a Reversed Field Pinch Device based on the External Magnetic Sensor Signals

Reconstruction of the Eddy Current Distribution on the Vacuum Vessel in a Reversed Field Pinch Device based on the External Magnetic Sensor Signals

Reconstruction of the eddy current profile on the vacuum vessel in a nuclear fusion device using only external magnetic sensor signals

A general algorithm for the numerical evaluation of nearly singular boundary integrals of various orders for two- and three-dimensional elasticity

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