IEEE Transactions on Microwave Theory and Techniques, ISSN 0018-9480, 10/2013, Volume 61, Issue 10, pp. 3503 - 3513

3-D hybrid finite-element (FE) boundary integral equation (BIE) formulations are widely used because of their ability to simulate large inhomogeneous...

hybrid finite-element boundary-integral equation (FE-BIE) | Dirichlet-to-Neumann (DtN) | Integral equations | Materials | Iron | Eigenvalues and eigenfunctions | Poincaré-Steklov (PS) | Mathematical model | internal resonances | Current | Equations | BOUNDARY-INTEGRAL METHODS | INTERIOR RESONANCES | FINITE-ELEMENT | Poincare-Steklov (PS) | ELECTROMAGNETIC SCATTERING | EQUATION | EFIE | ENGINEERING, ELECTRICAL & ELECTRONIC | Finite element method | Eigenfunctions | Mathematical models | Research | Analysis | Formulations | Operators | Computer simulation | Simulation | Boundaries | Three dimensional

hybrid finite-element boundary-integral equation (FE-BIE) | Dirichlet-to-Neumann (DtN) | Integral equations | Materials | Iron | Eigenvalues and eigenfunctions | Poincaré-Steklov (PS) | Mathematical model | internal resonances | Current | Equations | BOUNDARY-INTEGRAL METHODS | INTERIOR RESONANCES | FINITE-ELEMENT | Poincare-Steklov (PS) | ELECTROMAGNETIC SCATTERING | EQUATION | EFIE | ENGINEERING, ELECTRICAL & ELECTRONIC | Finite element method | Eigenfunctions | Mathematical models | Research | Analysis | Formulations | Operators | Computer simulation | Simulation | Boundaries | Three dimensional

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 12/2015, Volume 303, pp. 355 - 371

In the context of hybrid formulations, the Poincaré–Steklov operator acting on traces of solutions to the vector Helmholtz equation in a heterogeneous interior...

Calderón preconditioner | Schur complement discretization | Poincaré–Steklov operator | Heterogeneous domain | Electromagnetic scattering | Preconditioned hybrid formulation | Poincaré-Steklov operator | FINITE-ELEMENTS | ALGORITHM | DECOMPOSITION | 3D SCATTERING | PHYSICS, MATHEMATICAL | Poincare-Steklov operator | MFIE | Calderon preconditioner | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FIELD INTEGRAL-EQUATION | FORMULATIONS | FE-BI-MLFMA | SIMULATIONS | EFIE | Electromagnetism | Operators | Mathematical analysis | Exteriors | Mathematical models | Boundaries | Vectors (mathematics) | Boundary element method | Three dimensional

Calderón preconditioner | Schur complement discretization | Poincaré–Steklov operator | Heterogeneous domain | Electromagnetic scattering | Preconditioned hybrid formulation | Poincaré-Steklov operator | FINITE-ELEMENTS | ALGORITHM | DECOMPOSITION | 3D SCATTERING | PHYSICS, MATHEMATICAL | Poincare-Steklov operator | MFIE | Calderon preconditioner | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FIELD INTEGRAL-EQUATION | FORMULATIONS | FE-BI-MLFMA | SIMULATIONS | EFIE | Electromagnetism | Operators | Mathematical analysis | Exteriors | Mathematical models | Boundaries | Vectors (mathematics) | Boundary element method | Three dimensional

Journal Article

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, ISSN 1937-1632, 02/2019, Volume 12, Issue 1, pp. 1 - 26

In the framework of the Laplacian transport, described by a Robin boundary value problem in an exterior domain in R-n, we generalize the definition of the...

TRACE | MATHEMATICS, APPLIED | INEQUALITIES | SUBSETS | Laplacian transport | Poincare-Steklov operator | d-sets | SOBOLEV SPACES | fractal | LIPSCHITZ-SPACES | ASYMPTOTICS | BOUNDARY | DOMAINS

TRACE | MATHEMATICS, APPLIED | INEQUALITIES | SUBSETS | Laplacian transport | Poincare-Steklov operator | d-sets | SOBOLEV SPACES | fractal | LIPSCHITZ-SPACES | ASYMPTOTICS | BOUNDARY | DOMAINS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2016, Volume 436, Issue 1, pp. 467 - 477

A second order Schwarz method for elliptic partial differential equations is developed and analyzed at a continuous level, which can be parallel implemented...

Poincaré–Steklov operator | Schwarz methods | Energy estimates | Domain decomposition | Convergence analysis | Poincaré-Steklov operator | MATHEMATICS | MATHEMATICS, APPLIED | DOMAIN DECOMPOSITION METHOD | ALGORITHM | ARBITRARY INTERFACE | Poincare-Steklov operator | ABSORBING BOUNDARY-CONDITIONS | Analysis | Methods | Algorithms

Poincaré–Steklov operator | Schwarz methods | Energy estimates | Domain decomposition | Convergence analysis | Poincaré-Steklov operator | MATHEMATICS | MATHEMATICS, APPLIED | DOMAIN DECOMPOSITION METHOD | ALGORITHM | ARBITRARY INTERFACE | Poincare-Steklov operator | ABSORBING BOUNDARY-CONDITIONS | Analysis | Methods | Algorithms

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 02/2003, Volume 41, Issue 1, pp. 1 - 36

A method with optimal ( up to logarithmic terms) complexity for solving elliptic problems is proposed. The method relies on interior regularity, but the...

Meshes refined toward boundary | hp-finite element methods | Preconditioning | Data-sparse approximation to Poincaré-Steklov operator | MATHEMATICS, APPLIED | P-VERSION | REFINED MESHES | SPACES | EQUATIONS | 3 DIMENSIONS | operator | preconditioning | PIECEWISE ANALYTIC DATA | ELLIPTIC PROBLEMS | meshes refined toward boundary | REGULARITY | data-sparse approximation to Poincare-Steklov | OPERATORS | DOMAINS

Meshes refined toward boundary | hp-finite element methods | Preconditioning | Data-sparse approximation to Poincaré-Steklov operator | MATHEMATICS, APPLIED | P-VERSION | REFINED MESHES | SPACES | EQUATIONS | 3 DIMENSIONS | operator | preconditioning | PIECEWISE ANALYTIC DATA | ELLIPTIC PROBLEMS | meshes refined toward boundary | REGULARITY | data-sparse approximation to Poincare-Steklov | OPERATORS | DOMAINS

Journal Article

Mathematical Modelling and Analysis, ISSN 1392-6292, 01/2007, Volume 12, Issue 3, pp. 309 - 324

In this work finite superelements method (FSEM) for solution of biharmonic equation in bounded domains is proposed and developed. The method is based on...

finite superelements method | Biharmonic equation | Poincaré-Steklov operators | Finite superelements method | MATHEMATICS | Poincare-Steklov operators | biharmonic equation | Poincaré‐Steklov operators

finite superelements method | Biharmonic equation | Poincaré-Steklov operators | Finite superelements method | MATHEMATICS | Poincare-Steklov operators | biharmonic equation | Poincaré‐Steklov operators

Journal Article

SIAM Journal on Scientific Computing, ISSN 1064-8275, 2014, Volume 36, Issue 4, pp. A2023 - A2046

A numerical method for solving elliptic PDEs with variable coefficients on two-dimensional domains is presented. The method is based on high-order composite...

Nested dissection | Hierarchically block separable matrix | Multifrontal method | Dirichlet-to-Neumann operator | Reduction to interface | Fast direct solver | Poincaré-Steklov operator | High-order discretization | Multidomain spectral method | Structured matrix algebra | MATHEMATICS, APPLIED | ALGORITHM | INTEGRAL-EQUATIONS | reduction to interface | Poincare-Steklov operator | high-order discretization | structured matrix algebra | multifrontal method | multidomain spectral method | fast direct solver | nested dissection | hierarchically block separable matrix | Partial differential equations | Computation | Mathematical analysis | Solvers | Mathematical models | Spectra | Coefficients | Complexity

Nested dissection | Hierarchically block separable matrix | Multifrontal method | Dirichlet-to-Neumann operator | Reduction to interface | Fast direct solver | Poincaré-Steklov operator | High-order discretization | Multidomain spectral method | Structured matrix algebra | MATHEMATICS, APPLIED | ALGORITHM | INTEGRAL-EQUATIONS | reduction to interface | Poincare-Steklov operator | high-order discretization | structured matrix algebra | multifrontal method | multidomain spectral method | fast direct solver | nested dissection | hierarchically block separable matrix | Partial differential equations | Computation | Mathematical analysis | Solvers | Mathematical models | Spectra | Coefficients | Complexity

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2010, Volume 235, Issue 1, pp. 301 - 314

Optimized Schwarz methods form a class of domain decomposition methods for the solution of elliptic partial differential equations. Optimized Schwarz methods...

Optimized Schwarz methods | Poincare–Steklov operator | Lions nonoverlapping method | Convergence acceleration | Domain decomposition | PoincareSteklov operator | MATHEMATICS, APPLIED | DECOMPOSITION METHODS | Poincare-Steklov operator | ABSORBING BOUNDARY-CONDITIONS | Operators | Computer simulation | Discretization | Upper bounds | Domain decomposition methods | Fourier analysis | Mathematical models | Spectra | Convergence

Optimized Schwarz methods | Poincare–Steklov operator | Lions nonoverlapping method | Convergence acceleration | Domain decomposition | PoincareSteklov operator | MATHEMATICS, APPLIED | DECOMPOSITION METHODS | Poincare-Steklov operator | ABSORBING BOUNDARY-CONDITIONS | Operators | Computer simulation | Discretization | Upper bounds | Domain decomposition methods | Fourier analysis | Mathematical models | Spectra | Convergence

Journal Article

International Journal of Applied Electromagnetics and Mechanics, ISSN 1383-5416, 2004, Volume 19, Issue 1-4, pp. 63 - 67

We consider some inverse boundary problems which are to determine the coefficients or functions of elliptic differential equations inside the domain Omega from...

Poincaré-Steklov operator | Parameter identification | Oseen linearization | Schrödinger equation | Inverse problem | inverse problem | MECHANICS | PHYSICS, APPLIED | Schrodinger equation | BOUNDARY MEASUREMENTS | DETERMINING CONDUCTIVITY | Poincare-Steklov operator | parameter identification | ENGINEERING, ELECTRICAL & ELECTRONIC

Poincaré-Steklov operator | Parameter identification | Oseen linearization | Schrödinger equation | Inverse problem | inverse problem | MECHANICS | PHYSICS, APPLIED | Schrodinger equation | BOUNDARY MEASUREMENTS | DETERMINING CONDUCTIVITY | Poincare-Steklov operator | parameter identification | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 11/2016, Volume 289, Issue 16, pp. 1968 - 1985

This paper is devoted to classical spectral boundary value problems for strongly elliptic second‐order systems in bounded Lipschitz domains, in general...

Poincaré–Steklov spectral problem | Lipschitz domain | Abel–Lidskii summability | root functions | strong ellipticity | optimal resolvent estimate | spaces of Bessel potentials | 35P10 | completeness | Dirichlet and Neumann spectral problems | Poincare-Steklov spectral problem | BOUNDARY-VALUE-PROBLEMS | Abel-Lidskii summability | MATHEMATICS | BESOV | OPERATORS

Poincaré–Steklov spectral problem | Lipschitz domain | Abel–Lidskii summability | root functions | strong ellipticity | optimal resolvent estimate | spaces of Bessel potentials | 35P10 | completeness | Dirichlet and Neumann spectral problems | Poincare-Steklov spectral problem | BOUNDARY-VALUE-PROBLEMS | Abel-Lidskii summability | MATHEMATICS | BESOV | OPERATORS

Journal Article

IMA Journal of Numerical Analysis, ISSN 0272-4979, 10/2004, Volume 24, Issue 4, pp. 643 - 669

In this paper, we are concerned with the non-overlapping domain decomposition method with non-matching grids for three-dimensional elliptic equations. For this...

Inexact solver | Preconditioner | Mortar multiplier | Condition number | Poincaré-Steklov operator | Domain decomposition | Non-matching grids | ELLIPTIC PROBLEMS | MATHEMATICS, APPLIED | domain decomposition | CONVERGENCE | non-matching grids | mortar multiplier | SUBSTRUCTURING PRECONDITIONERS | inexact solver | preconditioner | FINITE-ELEMENT-METHOD | Poincare-Steklov operator | condition number

Inexact solver | Preconditioner | Mortar multiplier | Condition number | Poincaré-Steklov operator | Domain decomposition | Non-matching grids | ELLIPTIC PROBLEMS | MATHEMATICS, APPLIED | domain decomposition | CONVERGENCE | non-matching grids | mortar multiplier | SUBSTRUCTURING PRECONDITIONERS | inexact solver | preconditioner | FINITE-ELEMENT-METHOD | Poincare-Steklov operator | condition number

Journal Article

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 01/1997, Volume 66, Issue 217, pp. 125 - 138

This paper is concerned with the Poincaré-Steklov operator that is widely used in domain decomposition methods. It is proved that the inverse of the...

Inverted spectra | Triangulation | Boundary value problems | Approximation | Decomposition methods | Matrices | Preconditioning | Greens function | Vertices | Green's function | Poincaré-Steklov operator | Schur complement | Multigrid | Preconditioner | Domain decomposition | ELLIPTIC PROBLEMS | MATHEMATICS, APPLIED | DOMAIN DECOMPOSITION PRECONDITIONER | domain decomposition | multigrid | CONSTRUCTION | K PN MATHEMATICS, APPLIED | preconditioner | Poincare-Steklov operator

Inverted spectra | Triangulation | Boundary value problems | Approximation | Decomposition methods | Matrices | Preconditioning | Greens function | Vertices | Green's function | Poincaré-Steklov operator | Schur complement | Multigrid | Preconditioner | Domain decomposition | ELLIPTIC PROBLEMS | MATHEMATICS, APPLIED | DOMAIN DECOMPOSITION PRECONDITIONER | domain decomposition | multigrid | CONSTRUCTION | K PN MATHEMATICS, APPLIED | preconditioner | Poincare-Steklov operator

Journal Article

Electronic Transactions on Numerical Analysis, ISSN 1068-9613, 2009, Volume 36, pp. 168 - 194

Various forms of preconditioners for elliptic finite element matrices are studied, based on suitable block matrix partitionings. Bounds for the resulting...

Poincaré- steklov operator | Approximate block factorization | Schur complement | Domain decomposition | Preconditioning | Strengthened cauchy-schwarz-bunyakowski inequality | MATHEMATICS, APPLIED | domain decomposition | approximate block factorization | Poincare-Steklov operator | preconditioning | strengthened Cauchy-Schwarz-Bunyakowski inequality

Poincaré- steklov operator | Approximate block factorization | Schur complement | Domain decomposition | Preconditioning | Strengthened cauchy-schwarz-bunyakowski inequality | MATHEMATICS, APPLIED | domain decomposition | approximate block factorization | Poincare-Steklov operator | preconditioning | strengthened Cauchy-Schwarz-Bunyakowski inequality

Journal Article

Computational Methods in Applied Mathematics, ISSN 1609-4840, 10/2012, Volume 12, Issue 4, pp. 500 - 512

Journal Article

Computational Methods in Applied Mathematics, ISSN 1609-4840, 2001, Volume 7, Issue 1, pp. 3 - 24

This paper considers the Fedorenko Finite Superelement Method (FSEM) and some of its applications. The general idea, the main theoretical background, and the...

finite element method | Poincaré-Steklov operators | finite superelement method | equation for traces | Finite element method | Equation for traces | Finite superelement method

finite element method | Poincaré-Steklov operators | finite superelement method | equation for traces | Finite element method | Equation for traces | Finite superelement method

Journal Article

Numerical Algorithms, ISSN 1017-1398, 5/2009, Volume 51, Issue 1, pp. 115 - 131

Optimized Schwarz methods form a class of domain decomposition methods for the solution of elliptic partial differential equations. When the subdomains are...

35J20 | Poincaré–Steklov operator | Convergence acceleration | Numeric Computing | Optimized Schwarz methods | Theory of Computation | 65Y10 | Discontinuous coefficient | Algebra | Algorithms | Computer Science | Mathematics, general | Domain decomposition | 65N55 | 65N30 | Poincaré-Steklov operator | MATHEMATICS, APPLIED | HELMHOLTZ-EQUATION | OVERLAP | Poincare-Steklov operator | DOMAIN DECOMPOSITION METHODS | Operators | Partial differential equations | Domain decomposition methods | Fourier analysis | Mathematical models | Spectra | Estimates | Convergence

35J20 | Poincaré–Steklov operator | Convergence acceleration | Numeric Computing | Optimized Schwarz methods | Theory of Computation | 65Y10 | Discontinuous coefficient | Algebra | Algorithms | Computer Science | Mathematics, general | Domain decomposition | 65N55 | 65N30 | Poincaré-Steklov operator | MATHEMATICS, APPLIED | HELMHOLTZ-EQUATION | OVERLAP | Poincare-Steklov operator | DOMAIN DECOMPOSITION METHODS | Operators | Partial differential equations | Domain decomposition methods | Fourier analysis | Mathematical models | Spectra | Estimates | Convergence

Journal Article

17.
Full Text
Regularity of variational solutions to linear boundary value problems in Lipschitz domains

Functional Analysis and Its Applications, ISSN 0016-2663, 10/2006, Volume 40, Issue 4, pp. 313 - 329

In a bounded Lipschitz domain in ℝn, we consider a second-order strongly elliptic system with symmetric principal part written in divergent form. We study the...

interpolation | regularity of solutions | Functional Analysis | regularity of eigenfunctions | Analysis | Lebesgue xxx Besov spaces | Mathematics | Dirichlet, Neumann, xxx Poincaré-Steklov boundary value problems | variational solution | second-order strongly elliptic system | Interpolation | Neumann | Second-order strongly elliptic system | Regularity of solutions | Regularity of eigenfunctions | Variational solution | Dirichlet | Xxx Poincaré-Steklov boundary value problems | MATHEMATICS, APPLIED | SPACES | Lebesgue and Besov spaces | LAYER POTENTIALS | SOBOLEV | MATHEMATICS | and Poincare-Steklov boundary value problems | BESOV | DIRICHLET PROBLEM | ELLIPTIC-SYSTEMS | EQUATION | OPERATORS | RIEMANNIAN-MANIFOLDS

interpolation | regularity of solutions | Functional Analysis | regularity of eigenfunctions | Analysis | Lebesgue xxx Besov spaces | Mathematics | Dirichlet, Neumann, xxx Poincaré-Steklov boundary value problems | variational solution | second-order strongly elliptic system | Interpolation | Neumann | Second-order strongly elliptic system | Regularity of solutions | Regularity of eigenfunctions | Variational solution | Dirichlet | Xxx Poincaré-Steklov boundary value problems | MATHEMATICS, APPLIED | SPACES | Lebesgue and Besov spaces | LAYER POTENTIALS | SOBOLEV | MATHEMATICS | and Poincare-Steklov boundary value problems | BESOV | DIRICHLET PROBLEM | ELLIPTIC-SYSTEMS | EQUATION | OPERATORS | RIEMANNIAN-MANIFOLDS

Journal Article

2017 International Siberian Conference on Control and Communications (SIBCON), 06/2017, pp. 1 - 6

Power hardware-in-the-loop modeling (PHIL) is one of advanced approach for test automation and verification of complex circuits and systems. This approach is...

Couplings | Computational modeling | Signal processing algorithms | simulation | Interface algorithm | power hardware-in-the-loop | Stability analysis | Hardware | Numerical models | Mathematical model | stability | Poincare-Steklov operator | power hardware-in-The-loop

Couplings | Computational modeling | Signal processing algorithms | simulation | Interface algorithm | power hardware-in-the-loop | Stability analysis | Hardware | Numerical models | Mathematical model | stability | Poincare-Steklov operator | power hardware-in-The-loop

Conference Proceeding

IMA Journal of Numerical Analysis, ISSN 0272-4979, 4/2009, Volume 29, Issue 2, pp. 332 - 349

Lions' non-overlapping domain decomposition method for the solution of elliptic partial differential equations has been analysed extensively by many authors....

Optimized Schwarz methods | Convergence acceleration | Lions' non-overlapping method | Domain decomposition | Poincare-Steklov operator | MATHEMATICS, APPLIED | convergence acceleration | domain decomposition | optimized Schwarz methods | ITERATIVE PROCEDURE

Optimized Schwarz methods | Convergence acceleration | Lions' non-overlapping method | Domain decomposition | Poincare-Steklov operator | MATHEMATICS, APPLIED | convergence acceleration | domain decomposition | optimized Schwarz methods | ITERATIVE PROCEDURE

Journal Article

Computational Mathematics and Mathematical Physics, ISSN 0965-5425, 2/2006, Volume 46, Issue 2, pp. 258 - 270

Results of the theoretical and numerical studies of an algorithm based on the combined use of the finite element and finite superelement methods are presented....

Computational Mathematics and Numerical Analysis | Mathematics | Poincaré-Steklov operators | finite superelement method | Finite superelement method | Studies | Finite element analysis | Finite element method | Errors | Algorithms | Computation | Mathematical analysis | Laplace equation | Mathematical models | Estimates

Computational Mathematics and Numerical Analysis | Mathematics | Poincaré-Steklov operators | finite superelement method | Finite superelement method | Studies | Finite element analysis | Finite element method | Errors | Algorithms | Computation | Mathematical analysis | Laplace equation | Mathematical models | Estimates

Journal Article

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