A mixed-type finite element approximation for radiation problems using fictitious domain method

Nasir, H. M.; Kako, Tetsuya; Koyama, Daisuke

doi:10.1016/s0377-0427(02)00718-5

Cited by 7 publications

(8 citation statements)

References 17 publications

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“…In view of Theorem 3.2 (1) and (2), the functions y l (± 1/t 1 , ± t 2 /t 1 ), y l (± t 2 /t 1 , ± 1/t 1 ) and their symmetric counterparts are also solutions to (5). We now construct smoothly continuous spherical functions on S 2 as six-tuple of the solutions of the Laplace-Beltrami eigenvalue problem.…”

Section: Theorem 32mentioning

confidence: 99%

“…In two dimensions with polar co-ordinates, Nasir et al [5] used an artificial boundary with an artificial boundary condition around the polar origin in the domain of the Helmholtz equation and introduced a mixed type finite element method. Nasir and Kako [6] and Heikkola et al [7,8] have used rectangular co-ordinates near the origin and polar co-ordinates away from the origin for two-and three-dimensional problems.…”

Section: Introductionmentioning

confidence: 99%

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Spherical harmonics in a non‐polar co‐ordinate system and application to Fourier series in 2‐sphere

Nasir

2007

Math Methods in App Sciences

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SUMMARYA new non-polar spherical co-ordinate system for the three-dimensional space is introduced. The co-ordinate system is composed of six local co-ordinate systems mapped from six faces of a cube on to the 2-sphere. Weakly orthogonal and orthogonal spherical harmonics are constructed in this coordinate system. The spherical harmonics are easily computable functions consisting of polynomials and square root of polynomials. Examples of finite Fourier series computations are given in terms of the new spherical harmonics to demonstrate their immediate applicability.

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Section: Theorem 32mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Spherical harmonics in a non‐polar co‐ordinate system and application to Fourier series in 2‐sphere

Nasir

2007

Math Methods in App Sciences

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“…Representative works include the many contributions of Glowinski and his collaborators on flows with rigid bodies (Glowinski et al 1994b(Glowinski et al , 1997(Glowinski et al , 2001) and on other elliptic problems (Glowinski et al 1996;Glowinski and Kuznetsov 1998; see also Maitre and Tomas 1999). Applications of the fictitious domain method now cover an ever-widening spectrum, including work on unsteady problems (Collino et al 1997), fluidstructure interaction (Baaijens 2001), radiation and scattering problems for the Helmholtz operator (Heikkola et al 1998(Heikkola et al , 2003Nasir et al 2003), the recent work on the treatment of the exterior Helmholtz problem by Farhat and Hetmaniuk (2002) and by Farhat (2003a, 2003b), and the development of distributed forms of the fictitious domain method in which the constraints are imposed over regions as opposed to interfaces Patankar et al 2000). Applications to biomechanical problems are scantier (see De Hart et al (2000, 2003, for modelling of the aortic valve), despite the attractiveness of the method for these problems.…”

Section: Introductionmentioning

confidence: 99%

Assessment of a fictitious domain method for patient-specific biomechanical modelling of press-fit orthopaedic implantation

Kallivokas

Ghattas

et al. 2012

Computer Methods in Biomechanics and Biomedical Engineering

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In this article, we discuss an application of a fictitious domain method to the numerical simulation of the mechanical process induced by press-fitting cementless femoral implants in total hip replacement surgeries. Here, the primary goal is to demonstrate the feasibility of the method and its advantages over competing numerical methods for a wide range of applications for which the primary input originates from computed tomography-, magnetic resonance imaging- or other regular-grid medical imaging data. For this class of problems, the fictitious domain method is a natural choice, because it avoids the segmentation, surface reconstruction and meshing phases required by unstructured geometry-conforming simulation methods. We consider the implantation of a press-fit femoral artificial prosthesis as a prototype problem for sketching the application path of the methodology. Of concern is the assessment of the robustness and speed of the methodology, for both factors are critical if one were to consider patient-specific modelling. To this end, we report numerical results that exhibit optimal convergence rates and thus shed a favourable light on the approach.

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“…We can prove the theoretical convergence and the practical computational efficiency of this type of mixed method in the case of the DtN mapping (see Nasir et al [2003]). …”

Section: Application To Radiation Boundary Conditionmentioning

confidence: 89%

“…In the next subsection, we will briefly review the recent results of Nasir et al [2003] based on a mixed method approximation.…”

Section: Radiation Boundary Conditionsmentioning

confidence: 99%

Numerical Approximation of Dirichlet-to-Neumann Mapping and its Application to Voice Generation Problem

Kako

Touda

Lecture Notes in Computational Science and Engineering

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Summary. In this paper, we treat the numerical method for the Helmholtz equation in unbounded region with simple cylindrical or spherical shape outside some bounded region and apply the method to voice generation problem. The numerical method for the Helmholtz equation in unbounded region is based on the domain decomposition technique to divide the region into a bounded region and the rest unbounded one. We then treat the approximation of the artificial boundary condition given through the DtN mapping on the artificial boundary. We apply the finite element approximation to discretize the problem. In applying the method to the voice generation problem, it is essential to compute the frequency response function or the formant curve. We give variational formulas for the resolvent poles with respect to the variation of vocal tract boundary which determine the peaks of frequency response function known as formants, and we propose the use of variational formulas to design the location of formants.

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A mixed-type finite element approximation for radiation problems using fictitious domain method

Cited by 7 publications

References 17 publications

Spherical harmonics in a non‐polar co‐ordinate system and application to Fourier series in 2‐sphere

Spherical harmonics in a non‐polar co‐ordinate system and application to Fourier series in 2‐sphere

Assessment of a fictitious domain method for patient-specific biomechanical modelling of press-fit orthopaedic implantation

Numerical Approximation of Dirichlet-to-Neumann Mapping and its Application to Voice Generation Problem

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