C Method

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Gérard Granet - One of the best experts on this subject based on the ideXlab platform.

  • Coordinate Transformation Methods
    2012
    Co-Authors: Gérard Granet
    Abstract:

    The C-Method was born in the eighties in Clermont-Ferrand , FranCe, from the need to solve rigorously diffraCtion problems at Corrugated periodiC surfaCes in the resonanCe regime. The main diffiCulty of suCh problems is the matChing of boundaries Conditions. For that purpose, Chandezon et al introduCed the so Called translation Coordinate system in whiCh the boundary of the physiCal problem CoinCides with Coordinate surfaCes. The seCond ingredient of C-Method is to write Maxwell's equation under the Covariant form. This formulation Comes from relativity where the use of Curvilinear non orthogonal Coordinate system is essential and natural. The main feature of this formalism is that Maxwell's equations remain invariant in any Coordinate system, the geometry being shifted into the Constitutive relations. The third ingredient of C-Method is that it is a modal Method. This niCe property is linked with the translation Coordinate system in whiCh a diffraCtion problem may be expressed as an eigenvalue eigenveCtor problem with periodiC boundary Conditions. The key point of C-Method is the joint use of Curvilinear Coordinates and Covariant formulation of Maxwell's equations. All the new developments in the modeling of gratings like Adaptive Spatial Resolution, and MatChed Coordinates derive from this fundamental observation.

  • ANALYSIS OF CONICAL DIFFRACTION BY CURVED STRIP GRATINGS BY MEANS OF THE C-Method AND THE COMBINED BOUNDARY CONDITIONS Method
    Progress In Electromagnetics Research M, 2011
    Co-Authors: Gérard Granet, Faly Tinasoa, Karyl Raniriharinosy
    Abstract:

    A rigorous modal theory of ConiCal difiraCtion from Curved strip gratings is presented. In this approaCh, the C-Method with adaptive spatial resolution is used in ConjunCtion with the Combined boundary Conditions. The Method is suCCessfully validated by Comparison with a Case where the solution Can also be obtained in the Cartesian Coordinate system.

  • Study of eleCtromagnetiC diffraCtion by Curved strip gratings by use of the C-Method.
    Journal of the Optical Society of America. A Optics image science and vision, 2007
    Co-Authors: Brahim Guizal, Gérard Granet
    Abstract:

    The C-Method is one of the most effiCient and versatile Methods designed for diffraCtion gratings. Its strength lies in the use of a Coordinate system in whiCh the surfaCe of the grating CoinCides with a Coordinate surfaCe. The result is a great simplifiCation in writing the boundary Conditions. We exploit this simplifiCation to treat the problem of diffraCtion from Curved strip gratings, and we use the Combined boundary Conditions Method that has been introduCed for planar strip gratings and proved to be very effiCient.

  • C-Method: SEVERAL ASPECTS OF SPECTRAL THEORY OF GRATINGS
    Progress In Electromagnetics Research, 2006
    Co-Authors: A. Poyedinchuk, Yury A. Tuchkin, Nataliya P. Yashina, Jean Chandezon, Gérard Granet
    Abstract:

    The goal of the present paper is two folded. The first, the MethodologiCal one, is the Complementation of well established in diffraCtion theory of gratings C Method with Certain elements of speCtral theory and the development of interaCtive numeriCal algorithm that made feed baCk ConjunCtion between diffraCtion and speCtral problems. As a natural result the seCond goal appeared: the appearing of suCh tool for numeriCal experiments resulted in profound qualitative and quantitative study of rather peCuliar phenomena in resonant sCattering from periodiC surfaCe. SpeCial attention has been paid to the investigation of eleCtromagnetiC waves diffraCtion from periodiC boundaries of material with single and double negative parameters.

  • Rigorous and effiCient grating-analysis Method made easy for optiCal engineers
    Applied optics, 1999
    Co-Authors: Jean Chandezon, Gérard Granet, Jean-pierre Plumey
    Abstract:

    The Coordinate-transformation-based differential Method of Chandezon et al. [J. Opt. (Paris) 11, 235 (1980); J. Opt. SoC. Am. 72, 839 (1982)] (the C Method) is one of the simplest and most versatile Methods for modeling surfaCe-relief gratings. However, to date it has been used by only a small number of people, probably beCause, traditionally, elementary tensor theory is used to formulate the Method. We reformulate the C Method without using any knowledge of tensor, thus, we hope, making the C Method more aCCessible to optiCal engineers.

Richard Dusséaux - One of the best experts on this subject based on the ideXlab platform.

  • A Complex Mix-Shifted Parallel QR Algorithm for the C-Method
    Progress In Electromagnetics Research B, 2016
    Co-Authors: Cihui Pan, Richard Dusséaux, Nahid Emad
    Abstract:

    The C-Method is an exaCt Method for analyzing gratings and rough surfaCes. This Method leads to large-size dense Complex non-Hermitian eigenvalue. In this paper, we introduCe a parallel QR algorithm that is speCifiCally designed for the C-Method. We define the " early shift " for the matrix aCCording to the observed properties. We propose a Combination of the " early shift " , Wilkinson's shift and exCeptional shift together to aCCelerate ConvergenCe. First, we use the " early shift " in order to have quiCk deflation of some eigenvalues. The multi-window bulge Chain Chasing and parallel aggressive early deflation are used. This approaCh ensures that most Computations are performed in level 3 BLAS operations. The aggressive early deflation approaCh Can deteCt deflation muCh quiCker and aCCelerate ConvergenCe. Mixed MPI-Open MP teChniques are used for performing the Codes to hybrid shared and distributed memory platforms. We validate our approaCh by Comparison with experimental data for sCattering patterns of two-dimensional rough surfaCes.

  • The C-Method as an Initial Value Problem: AppliCation to Multilayer Gratings
    2015
    Co-Authors: Cihui Pan, Richard Dusséaux, Nahid Emad
    Abstract:

    We study our approaCh of the C-Method as an initial value problem for the effiCient CalCulation of the N-dimensional sCattering matrix of a grating. We apply this Method to multilayer gratings with an arbitrary number of interfaCes. The interfaCes Can have different funCtional form and amplitude and Can be parallel or not. For eaCh interfaCe separating two homogeneous media, we Consider two horizontal planes above and below the interfaCe, and define a Coordinate system suCh that the interfaCe and both horizontal planes Correspond to Coordinate surfaCes. Inside the area delimited by the two horizontal planes, the Maxwell's equations lead to an initial value problem whiCh Can be solved with initial Conditions satisfying the boundary Conditions. Outside this area, the fields are represented by Rayleigh expansion. The sCattering matrix between two ConseCutive media is obtained by using Continuity relations between different Components of fields on the horizontal planes. We Consider a n + 1 layer diffraCtion grating, thus there are n interfaCes separating the layers. From the uppermost to downmost, these layers are Composed of medium 1 to medium n + 1. EaCh medium has a Constant optiCal index. Thus we Can CalCulate the sCattering matrix Si,i+1 whiCh assoCiate the inComing and outComing waves from medium i and i + 1. Then we ColleCt all the sCattering matrix of adjaCent medium, Si,i+1, i = 1; : : : ; n and obtain the global matrix S1,n+1 by Combination of elementary matriCes Si,i+1, i = 1; : : : ; n. The proposed Method gives the e±CienCies with a good aCCuraCy. Experiments are performed on a three layer grating with interfaCes desCribed by TrigonometriC funCtions. We also study the anomalies of Coated dieleCtriC gratings.

  • Parallel QR Algorithm for the C-Method: AppliCation to the DiffraCtion by Gratings and Rough SurfaCes
    2015
    Co-Authors: Cihui Pan, Nahid Emad, Richard Dusséaux
    Abstract:

    The Curvilinear Coordinate Method (C-Method) is an exaCt Method for analysing of eleCtromagnetiC waves sCattering from rough surfaCes. It is based on Maxwell's equations under Covariant form written in a non-orthogonal Coordinate system. This Method leads to an eigenvalue system. All the eigenvalues and eigenveCtors of the sCattering matrix are required. The QR algorithm seems to be a suitable solution for this high dimension, dense, non-symmetriC and Complex sCattering matrix. In this paper, we present the parallel QR algorithm that is speCifiCally designed for the C-Method. We define the "early shift" for the sCattering matrix aCCording to the property that we have observed. We mixed the "early shift", Wilkinson's shift and exCeptional shift together to aCCelerate the ConvergenCe. EspeCially, we use the "early shift" first in order to have quiCk deflation of the real eigenvalues of the sCattering matrix. The multi-window bulge Chain Chasing and parallel aggressive early deflation are used. The multi-window bulge Chain Chasing approaCh ensures that most Computations are performed in 3 BLAS operations. The aggressive early deflation approaCh Can deteCt deflation muCh quiCker and thus aCCelerate ConvergenCe. Mixed MPI-OpenMP teChniques are utilized for performing the Codes to distributed memory platforms. NumeriCal experiments are performed and appliCations of this parallel QR algorithm are applied to a real physiCal problem of diffraCtion.

  • SpringSim (HPS) - Parallel QR algorithm for the C-Method: appliCation to the diffraCtion by gratings and rough surfaCes
    2015
    Co-Authors: Cihui Pan, Nahid Emad, Richard Dusséaux
    Abstract:

    The Curvilinear Coordinate Method (C-Method) is an exaCt Method for analysing of eleCtromagnetiC waves sCattering from rough surfaCes. It is based on Maxwell's equations under Covariant form written in a non-orthogonal Coordinate system. This Method leads to an eigenvalue system. All the eigenvalues and eigenveCtors of the sCattering matrix are required. The QR algorithm seems to be a suitable solution for this high dimension, dense, non-symmetriC and Complex sCattering matrix. In this paper, we present the parallel QR algorithm that is speCifiCally designed for the C-Method. We define the "early shift" for the sCattering matrix aCCording to the property that we have observed. We mixed the "early shift", Wilkinson's shift and exCeptional shift together to aCCelerate the ConvergenCe. EspeCially, we use the "early shift" first in order to have quiCk deflation of the real eigenvalues of the sCattering matrix. The multi-window bulge Chain Chasing and parallel aggressive early deflation are used. The multi-window bulge Chain Chasing approaCh ensures that most Computations are performed in 3 BLAS operations. The aggressive early deflation approaCh Can deteCt deflation muCh quiCker and thus aCCelerate ConvergenCe. Mixed MPI-OpenMP teChniques are utilized for performing the Codes to distributed memory platforms. NumeriCal experiments are performed and appliCations of this parallel QR algorithm are applied to a real physiCal problem of diffraCtion.

  • Curvilinear Coordinate Method as an initial value problem: appliCation to gratings
    Journal of the Optical Society of America. A Optics Image Science and Vision, 2015
    Co-Authors: Cihui Pan, Richard Dusséaux, Mandiaye Fall, Nahid Emad
    Abstract:

    We propose a C-Method approaCh for the effiCient CalCulation of the sCattering matrix of a grating. We Consider two horizontal planes above and below the grating and define a Coordinate system suCh that the grating surfaCe and both horizontal planes Correspond to surfaCe Coordinates. Inside the area A delimited by the horizontal planes, the Covariant formalism of Maxwell’s equations leads to an initial value problem that is solved for independent initial Conditions satisfying the boundary Conditions. Outside the area A, the fields are represented by Rayleigh expansions. The sCattering matrix is obtained by using Continuity relations between different Components of fields on the horizontal planes.

Nahid Emad - One of the best experts on this subject based on the ideXlab platform.

  • A Complex Mix-Shifted Parallel QR Algorithm for the C-Method
    Progress In Electromagnetics Research B, 2016
    Co-Authors: Cihui Pan, Richard Dusséaux, Nahid Emad
    Abstract:

    The C-Method is an exaCt Method for analyzing gratings and rough surfaCes. This Method leads to large-size dense Complex non-Hermitian eigenvalue. In this paper, we introduCe a parallel QR algorithm that is speCifiCally designed for the C-Method. We define the " early shift " for the matrix aCCording to the observed properties. We propose a Combination of the " early shift " , Wilkinson's shift and exCeptional shift together to aCCelerate ConvergenCe. First, we use the " early shift " in order to have quiCk deflation of some eigenvalues. The multi-window bulge Chain Chasing and parallel aggressive early deflation are used. This approaCh ensures that most Computations are performed in level 3 BLAS operations. The aggressive early deflation approaCh Can deteCt deflation muCh quiCker and aCCelerate ConvergenCe. Mixed MPI-Open MP teChniques are used for performing the Codes to hybrid shared and distributed memory platforms. We validate our approaCh by Comparison with experimental data for sCattering patterns of two-dimensional rough surfaCes.

  • The C-Method as an Initial Value Problem: AppliCation to Multilayer Gratings
    2015
    Co-Authors: Cihui Pan, Richard Dusséaux, Nahid Emad
    Abstract:

    We study our approaCh of the C-Method as an initial value problem for the effiCient CalCulation of the N-dimensional sCattering matrix of a grating. We apply this Method to multilayer gratings with an arbitrary number of interfaCes. The interfaCes Can have different funCtional form and amplitude and Can be parallel or not. For eaCh interfaCe separating two homogeneous media, we Consider two horizontal planes above and below the interfaCe, and define a Coordinate system suCh that the interfaCe and both horizontal planes Correspond to Coordinate surfaCes. Inside the area delimited by the two horizontal planes, the Maxwell's equations lead to an initial value problem whiCh Can be solved with initial Conditions satisfying the boundary Conditions. Outside this area, the fields are represented by Rayleigh expansion. The sCattering matrix between two ConseCutive media is obtained by using Continuity relations between different Components of fields on the horizontal planes. We Consider a n + 1 layer diffraCtion grating, thus there are n interfaCes separating the layers. From the uppermost to downmost, these layers are Composed of medium 1 to medium n + 1. EaCh medium has a Constant optiCal index. Thus we Can CalCulate the sCattering matrix Si,i+1 whiCh assoCiate the inComing and outComing waves from medium i and i + 1. Then we ColleCt all the sCattering matrix of adjaCent medium, Si,i+1, i = 1; : : : ; n and obtain the global matrix S1,n+1 by Combination of elementary matriCes Si,i+1, i = 1; : : : ; n. The proposed Method gives the e±CienCies with a good aCCuraCy. Experiments are performed on a three layer grating with interfaCes desCribed by TrigonometriC funCtions. We also study the anomalies of Coated dieleCtriC gratings.

  • Parallel QR Algorithm for the C-Method: AppliCation to the DiffraCtion by Gratings and Rough SurfaCes
    2015
    Co-Authors: Cihui Pan, Nahid Emad, Richard Dusséaux
    Abstract:

    The Curvilinear Coordinate Method (C-Method) is an exaCt Method for analysing of eleCtromagnetiC waves sCattering from rough surfaCes. It is based on Maxwell's equations under Covariant form written in a non-orthogonal Coordinate system. This Method leads to an eigenvalue system. All the eigenvalues and eigenveCtors of the sCattering matrix are required. The QR algorithm seems to be a suitable solution for this high dimension, dense, non-symmetriC and Complex sCattering matrix. In this paper, we present the parallel QR algorithm that is speCifiCally designed for the C-Method. We define the "early shift" for the sCattering matrix aCCording to the property that we have observed. We mixed the "early shift", Wilkinson's shift and exCeptional shift together to aCCelerate the ConvergenCe. EspeCially, we use the "early shift" first in order to have quiCk deflation of the real eigenvalues of the sCattering matrix. The multi-window bulge Chain Chasing and parallel aggressive early deflation are used. The multi-window bulge Chain Chasing approaCh ensures that most Computations are performed in 3 BLAS operations. The aggressive early deflation approaCh Can deteCt deflation muCh quiCker and thus aCCelerate ConvergenCe. Mixed MPI-OpenMP teChniques are utilized for performing the Codes to distributed memory platforms. NumeriCal experiments are performed and appliCations of this parallel QR algorithm are applied to a real physiCal problem of diffraCtion.

  • SpringSim (HPS) - Parallel QR algorithm for the C-Method: appliCation to the diffraCtion by gratings and rough surfaCes
    2015
    Co-Authors: Cihui Pan, Nahid Emad, Richard Dusséaux
    Abstract:

    The Curvilinear Coordinate Method (C-Method) is an exaCt Method for analysing of eleCtromagnetiC waves sCattering from rough surfaCes. It is based on Maxwell's equations under Covariant form written in a non-orthogonal Coordinate system. This Method leads to an eigenvalue system. All the eigenvalues and eigenveCtors of the sCattering matrix are required. The QR algorithm seems to be a suitable solution for this high dimension, dense, non-symmetriC and Complex sCattering matrix. In this paper, we present the parallel QR algorithm that is speCifiCally designed for the C-Method. We define the "early shift" for the sCattering matrix aCCording to the property that we have observed. We mixed the "early shift", Wilkinson's shift and exCeptional shift together to aCCelerate the ConvergenCe. EspeCially, we use the "early shift" first in order to have quiCk deflation of the real eigenvalues of the sCattering matrix. The multi-window bulge Chain Chasing and parallel aggressive early deflation are used. The multi-window bulge Chain Chasing approaCh ensures that most Computations are performed in 3 BLAS operations. The aggressive early deflation approaCh Can deteCt deflation muCh quiCker and thus aCCelerate ConvergenCe. Mixed MPI-OpenMP teChniques are utilized for performing the Codes to distributed memory platforms. NumeriCal experiments are performed and appliCations of this parallel QR algorithm are applied to a real physiCal problem of diffraCtion.

  • Curvilinear Coordinate Method as an initial value problem: appliCation to gratings
    Journal of the Optical Society of America. A Optics Image Science and Vision, 2015
    Co-Authors: Cihui Pan, Richard Dusséaux, Mandiaye Fall, Nahid Emad
    Abstract:

    We propose a C-Method approaCh for the effiCient CalCulation of the sCattering matrix of a grating. We Consider two horizontal planes above and below the grating and define a Coordinate system suCh that the grating surfaCe and both horizontal planes Correspond to surfaCe Coordinates. Inside the area A delimited by the horizontal planes, the Covariant formalism of Maxwell’s equations leads to an initial value problem that is solved for independent initial Conditions satisfying the boundary Conditions. Outside the area A, the fields are represented by Rayleigh expansions. The sCattering matrix is obtained by using Continuity relations between different Components of fields on the horizontal planes.

Cihui Pan - One of the best experts on this subject based on the ideXlab platform.

  • A Complex Mix-Shifted Parallel QR Algorithm for the C-Method
    Progress In Electromagnetics Research B, 2016
    Co-Authors: Cihui Pan, Richard Dusséaux, Nahid Emad
    Abstract:

    The C-Method is an exaCt Method for analyzing gratings and rough surfaCes. This Method leads to large-size dense Complex non-Hermitian eigenvalue. In this paper, we introduCe a parallel QR algorithm that is speCifiCally designed for the C-Method. We define the " early shift " for the matrix aCCording to the observed properties. We propose a Combination of the " early shift " , Wilkinson's shift and exCeptional shift together to aCCelerate ConvergenCe. First, we use the " early shift " in order to have quiCk deflation of some eigenvalues. The multi-window bulge Chain Chasing and parallel aggressive early deflation are used. This approaCh ensures that most Computations are performed in level 3 BLAS operations. The aggressive early deflation approaCh Can deteCt deflation muCh quiCker and aCCelerate ConvergenCe. Mixed MPI-Open MP teChniques are used for performing the Codes to hybrid shared and distributed memory platforms. We validate our approaCh by Comparison with experimental data for sCattering patterns of two-dimensional rough surfaCes.

  • DiffraCtion éleCtromagnétique par des réseaux et des surfaCes rugueuses aléatoires : mise en œuvre deméthodes hautement effiCaCes pour la résolution de systèmes aux valeurs propres et de problèmesaux Conditions initiales
    2015
    Co-Authors: Cihui Pan
    Abstract:

    We study the eleCtromagnetiC diffraCtion by gratings and random rough surfaCes. The C-Method is an exaCt Method developed for this aim. It is based on Maxwell’s equations under Covariant form written in a nonorthogonal Coordinate system. The C-Method leads to an eigenvalue problem, the solution of whiCh gives the diffraCted field.We foCus on the numeriCal aspeCt of the C-Method, trying to develop an effiCient appliCation of this exaCt Method. For gratings, we have developed a new version of C-Method whiCh leads to a differential system with initial Conditions. This new version of C-Method Can be used to study multilayer gratings with homogeneous medium.We implemented high performanCe algorithms to the original versions of C-Method. EspeCially, we have developed a speCifiCally designed parallel QR algorithm for the C- Method and speCtral projeCtion Method to solve the eigenvalue problem more effiCiently. Experiments have shown that the Computation time Can be reduCed signifiCantly.

  • The C-Method as an Initial Value Problem: AppliCation to Multilayer Gratings
    2015
    Co-Authors: Cihui Pan, Richard Dusséaux, Nahid Emad
    Abstract:

    We study our approaCh of the C-Method as an initial value problem for the effiCient CalCulation of the N-dimensional sCattering matrix of a grating. We apply this Method to multilayer gratings with an arbitrary number of interfaCes. The interfaCes Can have different funCtional form and amplitude and Can be parallel or not. For eaCh interfaCe separating two homogeneous media, we Consider two horizontal planes above and below the interfaCe, and define a Coordinate system suCh that the interfaCe and both horizontal planes Correspond to Coordinate surfaCes. Inside the area delimited by the two horizontal planes, the Maxwell's equations lead to an initial value problem whiCh Can be solved with initial Conditions satisfying the boundary Conditions. Outside this area, the fields are represented by Rayleigh expansion. The sCattering matrix between two ConseCutive media is obtained by using Continuity relations between different Components of fields on the horizontal planes. We Consider a n + 1 layer diffraCtion grating, thus there are n interfaCes separating the layers. From the uppermost to downmost, these layers are Composed of medium 1 to medium n + 1. EaCh medium has a Constant optiCal index. Thus we Can CalCulate the sCattering matrix Si,i+1 whiCh assoCiate the inComing and outComing waves from medium i and i + 1. Then we ColleCt all the sCattering matrix of adjaCent medium, Si,i+1, i = 1; : : : ; n and obtain the global matrix S1,n+1 by Combination of elementary matriCes Si,i+1, i = 1; : : : ; n. The proposed Method gives the e±CienCies with a good aCCuraCy. Experiments are performed on a three layer grating with interfaCes desCribed by TrigonometriC funCtions. We also study the anomalies of Coated dieleCtriC gratings.

  • Parallel QR Algorithm for the C-Method: AppliCation to the DiffraCtion by Gratings and Rough SurfaCes
    2015
    Co-Authors: Cihui Pan, Nahid Emad, Richard Dusséaux
    Abstract:

    The Curvilinear Coordinate Method (C-Method) is an exaCt Method for analysing of eleCtromagnetiC waves sCattering from rough surfaCes. It is based on Maxwell's equations under Covariant form written in a non-orthogonal Coordinate system. This Method leads to an eigenvalue system. All the eigenvalues and eigenveCtors of the sCattering matrix are required. The QR algorithm seems to be a suitable solution for this high dimension, dense, non-symmetriC and Complex sCattering matrix. In this paper, we present the parallel QR algorithm that is speCifiCally designed for the C-Method. We define the "early shift" for the sCattering matrix aCCording to the property that we have observed. We mixed the "early shift", Wilkinson's shift and exCeptional shift together to aCCelerate the ConvergenCe. EspeCially, we use the "early shift" first in order to have quiCk deflation of the real eigenvalues of the sCattering matrix. The multi-window bulge Chain Chasing and parallel aggressive early deflation are used. The multi-window bulge Chain Chasing approaCh ensures that most Computations are performed in 3 BLAS operations. The aggressive early deflation approaCh Can deteCt deflation muCh quiCker and thus aCCelerate ConvergenCe. Mixed MPI-OpenMP teChniques are utilized for performing the Codes to distributed memory platforms. NumeriCal experiments are performed and appliCations of this parallel QR algorithm are applied to a real physiCal problem of diffraCtion.

  • SpringSim (HPS) - Parallel QR algorithm for the C-Method: appliCation to the diffraCtion by gratings and rough surfaCes
    2015
    Co-Authors: Cihui Pan, Nahid Emad, Richard Dusséaux
    Abstract:

    The Curvilinear Coordinate Method (C-Method) is an exaCt Method for analysing of eleCtromagnetiC waves sCattering from rough surfaCes. It is based on Maxwell's equations under Covariant form written in a non-orthogonal Coordinate system. This Method leads to an eigenvalue system. All the eigenvalues and eigenveCtors of the sCattering matrix are required. The QR algorithm seems to be a suitable solution for this high dimension, dense, non-symmetriC and Complex sCattering matrix. In this paper, we present the parallel QR algorithm that is speCifiCally designed for the C-Method. We define the "early shift" for the sCattering matrix aCCording to the property that we have observed. We mixed the "early shift", Wilkinson's shift and exCeptional shift together to aCCelerate the ConvergenCe. EspeCially, we use the "early shift" first in order to have quiCk deflation of the real eigenvalues of the sCattering matrix. The multi-window bulge Chain Chasing and parallel aggressive early deflation are used. The multi-window bulge Chain Chasing approaCh ensures that most Computations are performed in 3 BLAS operations. The aggressive early deflation approaCh Can deteCt deflation muCh quiCker and thus aCCelerate ConvergenCe. Mixed MPI-OpenMP teChniques are utilized for performing the Codes to distributed memory platforms. NumeriCal experiments are performed and appliCations of this parallel QR algorithm are applied to a real physiCal problem of diffraCtion.

Shuhua Yang - One of the best experts on this subject based on the ideXlab platform.

  • CorreCtion to: ArthrosCopiC release using F and C Method versus Conventional open release Method in the treatment of gluteal musCle ContraCture: a Comparative study.
    BMC musculoskeletal disorders, 2018
    Co-Authors: Saroj Rai, Chunqing Meng, Nabin Chaudhary, Nira Tamang, Xianzhe Liu, Hong Wang, Shengyang Jin, Xiaohong Wang, Shuhua Yang
    Abstract:

    Upon publiCation of this artiCle [1], it was requested that: the Corresponding author, Hong Wang's affiliation address be Changed from.

  • ArthrosCopiC release using F and C Method versus Conventional open release Method in the treatment of gluteal musCle ContraCture: a Comparative study
    BMC musculoskeletal disorders, 2017
    Co-Authors: Saroj Rai, Jin Shengyang, Chunqing Meng, Nabin Chaudhary, Nira Tamang, Wang Xiaohong, Xianzhe Liu, Hong Wang, Shuhua Yang
    Abstract:

    Gluteal musCle ContraCture (GMC), a debilitating disease, usually starts in early Childhood after variable dose of injeCtions around the buttoCk, if left untreated it worsens gradually and persists throughout the life. BeCause the disease mostly affeCts adolesCents and adults, there is always an aesthetiC ConCerns. Purposeof the study was to introduCe the arthrosCopiC F and C Method of GMC release, and to Compare its CliniCal effiCienCy with Conventional open surgery in terms of CliniCal outCome, rate of CompliCations, patient's satisfaCtions, and reCurrenCe. Between Jan 2013 and July 2015, 75 patients reCeived an arthrosCopiC release with F and C release Method and 71 patients reCeived Conventional open release of GMC. Primary surgeries in 16 years or older patients were inCluded in the study. Two groups were Compared CliniCally using Hip OutCome SCores - ACtivities of Daily Living SubsCale (HOS-ADL), Hip OutCome SCores - Sports SubsCale (HOS-Sports), Visual Analogue SCale (VAS), and Ye et al. evaluation Criteria. No statistiCally signifiCant differenCes were observed in Hip OutCome SCores - ACtivities of Daily Living SubsCale (HOS-ADL) (P = 0.078), Hip OutCome SCores - Sports SubsCale (HOS-Sports) (P = 0.340), and Visual Analogue SCale (VAS) (P = 0.524) between the two groups. 74 (98.7%) patients in the arthrosCopiC surgery group had good to exCellent results, whereas 69 (97.1%) patients in the Conventional open surgery group had good to exCellent results (P = 0.727). No statistiCally signifiCant differenCe was observed in reCurrenCe rate (P = 0.612). StatistiCally signifiCant differenCes were observed in inCision length, use of post-operative analgesia, post-operative off-bed aCtivity, and hospital stay. CompliCations were signifiCantly higher in the Conventional open surgery group (n = 21) than in the arthrosCopiC surgery group (n = 10) (P = 0.016). More importantly, CosmetiC satisfaCtion was 100% in arthrosCopiC release group, whereas only 71% had CosmetiC satisfaCtion in Conventional open surgery group (P < 0.001). Both, arthrosCopiC surgery and Conventional open surgery, are highly effeCtive tools for the GMC release in adolesCent and adult patients. ArthrosCopiC GMC release with F and C Method allows preCise and seleCtive release of ContraCture bands with small surgiCal trauma resulting fewer CompliCations, high CosmetiC satisfaCtion and minimal reCurrenCe.