Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 11/2013, Volume 46, Issue 43, pp. 435203 - 32

We propose a reformulation of the boundary integral equations for the Helmholtz equation in a domain in terms of incoming and outgoing boundary waves. We...

WHISPERING-GALLERY MODES | SECTION METHOD | SCATTERING APPROACH | CHAOTIC BILLIARDS | PHYSICS, MULTIDISCIPLINARY | ELEMENT METHOD | SEMICLASSICAL QUANTIZATION | QUANTUM SURFACE | GEOMETRICAL-THEORY | RAY | WAVE CHAOS | PHYSICS, MATHEMATICAL | Helmholtz equations | Operators | Wave propagation | Integral equations | Mathematical analysis | Dirichlet problem | Boundary conditions | Decomposition | Boundaries

WHISPERING-GALLERY MODES | SECTION METHOD | SCATTERING APPROACH | CHAOTIC BILLIARDS | PHYSICS, MULTIDISCIPLINARY | ELEMENT METHOD | SEMICLASSICAL QUANTIZATION | QUANTUM SURFACE | GEOMETRICAL-THEORY | RAY | WAVE CHAOS | PHYSICS, MATHEMATICAL | Helmholtz equations | Operators | Wave propagation | Integral equations | Mathematical analysis | Dirichlet problem | Boundary conditions | Decomposition | Boundaries

Journal Article

Journal of computational physics, ISSN 0021-9991, 2013, Volume 241, pp. 240 - 252

A new domain decomposition method is introduced for the heterogeneous 2-D and 3-D Helmholtz equations...

Helmholtz equation | Perfectly matched layers | Domain decomposition | High-frequency waves | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ALGORITHM | PRECONDITIONER | SOLVER | PHYSICS, MATHEMATICAL | MAXWELLS EQUATIONS | WAVE-PROPAGATION | Helmholtz equations | Subdivisions | Solvers | Domain decomposition methods | Reflection | Iterative methods | Three dimensional

Helmholtz equation | Perfectly matched layers | Domain decomposition | High-frequency waves | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ALGORITHM | PRECONDITIONER | SOLVER | PHYSICS, MATHEMATICAL | MAXWELLS EQUATIONS | WAVE-PROPAGATION | Helmholtz equations | Subdivisions | Solvers | Domain decomposition methods | Reflection | Iterative methods | Three dimensional

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 8/2018, Volume 76, Issue 2, pp. 727 - 758

...J Sci Comput (2018) 76:727–758 https://doi.org/10.1007/s10915-017-0638-x A Stable and Convergent Hodge Decomposition Method for Fluid–Solid Interaction...

Computational Mathematics and Numerical Analysis | Theoretical, Mathematical and Computational Physics | 65N06 | Helmholtz–Hodge decomposition | Mathematics | Primary 76D03 | 76M20 | 35J25 | Extended Hodge decomposition | Algorithms | Numerical analysis | Secondary 35Q30 | Mathematical and Computational Engineering | Fluid–solid interaction | FREE-SURFACE | Fluid-solid interaction | MATHEMATICS, APPLIED | MONOLITHIC APPROACH | FLOWS | SOLVERS | IMMERSED BOUNDARY METHOD | Helmholtz-Hodge decomposition | SCHEMES | Analysis | Methods | Force and energy

Computational Mathematics and Numerical Analysis | Theoretical, Mathematical and Computational Physics | 65N06 | Helmholtz–Hodge decomposition | Mathematics | Primary 76D03 | 76M20 | 35J25 | Extended Hodge decomposition | Algorithms | Numerical analysis | Secondary 35Q30 | Mathematical and Computational Engineering | Fluid–solid interaction | FREE-SURFACE | Fluid-solid interaction | MATHEMATICS, APPLIED | MONOLITHIC APPROACH | FLOWS | SOLVERS | IMMERSED BOUNDARY METHOD | Helmholtz-Hodge decomposition | SCHEMES | Analysis | Methods | Force and energy

Journal Article

Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 05/2019, Volume 39, Issue 5, pp. 2437 - 2454

The Helmholtz-Hodge decomposition (HHD) is applied to the construction of Lyapunov functions...

Potential functions | Strict orthogonality | Gradient vector fields | Lyapunov functions | Helmholtz-Hodge decomposition | MATHEMATICS | MATHEMATICS, APPLIED | potential functions | LIENARD SYSTEMS | strict orthogonality | gradient vector fields

Potential functions | Strict orthogonality | Gradient vector fields | Lyapunov functions | Helmholtz-Hodge decomposition | MATHEMATICS | MATHEMATICS, APPLIED | potential functions | LIENARD SYSTEMS | strict orthogonality | gradient vector fields

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 01/2015, Volume 280, pp. 232 - 247

The time-harmonic Maxwell equations describe the propagation of electromagnetic waves and are therefore fundamental for the simulation of many modern devices...

Transmission conditions | Optimized Schwarz methods | Maxwell equations | EDGE ELEMENT APPROXIMATIONS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | VERSION | PHYSICS, MATHEMATICAL | Algorithms | Electromagnetism | Analysis | Electromagnetic waves | Electric waves | Electromagnetic radiation | Magnetic fields | Methods | Helmholtz equations | Computer simulation | Mathematical analysis | Domain decomposition methods | Mathematical models | Maxwell's equations | Maxwell equation | Modeling and Simulation | Computer Science

Transmission conditions | Optimized Schwarz methods | Maxwell equations | EDGE ELEMENT APPROXIMATIONS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | VERSION | PHYSICS, MATHEMATICAL | Algorithms | Electromagnetism | Analysis | Electromagnetic waves | Electric waves | Electromagnetic radiation | Magnetic fields | Methods | Helmholtz equations | Computer simulation | Mathematical analysis | Domain decomposition methods | Mathematical models | Maxwell's equations | Maxwell equation | Modeling and Simulation | Computer Science

Journal Article

International journal for numerical methods in fluids, ISSN 0271-2091, 2015, Volume 78, Issue 1, pp. 37 - 62

SummaryA principal interval decomposition (PID) approach is presented for the reduced...

Kelvin–Helmholtz instability | Boussinesq equations | proper orthogonal decomposition | convection‐dominated flows | principal interval decomposition | reduced‐order modeling | Convection-dominated flows | Proper orthogonal decomposition | Kelvin-Helmholtz instability | Reduced-order modeling | Principal interval decomposition | DYNAMICAL MODEL | FINITE-DIFFERENCE SCHEMES | PHYSICS, FLUIDS & PLASMAS | STABILITY | REPRESENTATION | reduced-order modeling | convection-dominated flows | COMPACT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | RAYLEIGH-BENARD CONVECTION | Intervals | Windows (intervals) | Construction | Accuracy | Mathematical models | Decomposition | Unsteady | Proper Orthogonal Decomposition

Kelvin–Helmholtz instability | Boussinesq equations | proper orthogonal decomposition | convection‐dominated flows | principal interval decomposition | reduced‐order modeling | Convection-dominated flows | Proper orthogonal decomposition | Kelvin-Helmholtz instability | Reduced-order modeling | Principal interval decomposition | DYNAMICAL MODEL | FINITE-DIFFERENCE SCHEMES | PHYSICS, FLUIDS & PLASMAS | STABILITY | REPRESENTATION | reduced-order modeling | convection-dominated flows | COMPACT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | RAYLEIGH-BENARD CONVECTION | Intervals | Windows (intervals) | Construction | Accuracy | Mathematical models | Decomposition | Unsteady | Proper Orthogonal Decomposition

Journal Article

Granular matter, ISSN 1434-5021, 2018, Volume 20, Issue 3, pp. 1 - 24

...–Hodge decomposition of the displacement vector field obtained with DEM was used. The variational discrete multiscale vector field decomposition allowed for separating a vector field into the sum of three uniquely defined components...

Shear localization | Materials Science, general | Engineering Thermodynamics, Heat and Mass Transfer | Helmholtz–Hodge decomposition | Discrete element method | Physics | Geoengineering, Foundations, Hydraulics | Soft and Granular Matter, Complex Fluids and Microfluidics | Granular material | Engineering Fluid Dynamics | Vortex structure | Industrial Chemistry/Chemical Engineering | Plane strain compression | SAND | MECHANICS | PHYSICS, APPLIED | EVOLUTION | MATERIALS SCIENCE, MULTIDISCIPLINARY | MODEL | Helmholtz-Hodge decomposition | Analysis | Green technology | Economic models | Divergence | Sand | Deformation | Computer simulation | Vortices | Plane strain | Decomposition | Localization | Shear zone

Shear localization | Materials Science, general | Engineering Thermodynamics, Heat and Mass Transfer | Helmholtz–Hodge decomposition | Discrete element method | Physics | Geoengineering, Foundations, Hydraulics | Soft and Granular Matter, Complex Fluids and Microfluidics | Granular material | Engineering Fluid Dynamics | Vortex structure | Industrial Chemistry/Chemical Engineering | Plane strain compression | SAND | MECHANICS | PHYSICS, APPLIED | EVOLUTION | MATERIALS SCIENCE, MULTIDISCIPLINARY | MODEL | Helmholtz-Hodge decomposition | Analysis | Green technology | Economic models | Divergence | Sand | Deformation | Computer simulation | Vortices | Plane strain | Decomposition | Localization | Shear zone

Journal Article

Science China Information Sciences, ISSN 1674-733X, 1/2019, Volume 62, Issue 1, pp. 1 - 13

The symmetry-based decompositions of finite games are investigated. First, the vector space of finite games is decomposed into a symmetric subspace and an orthogonal complement of the symmetric subspace...

Computer Science | Nash equilibrium | Information Systems and Communication Service | decomposition | potential game | symmetric game | semi-tensor product of matrices | COMPUTER SCIENCE, INFORMATION SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC

Computer Science | Nash equilibrium | Information Systems and Communication Service | decomposition | potential game | symmetric game | semi-tensor product of matrices | COMPUTER SCIENCE, INFORMATION SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

9.
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Domain decomposition preconditioning for high-frequency Helmholtz problems with absorption

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 09/2017, Volume 86, Issue 307, pp. 2089 - 2127

In this paper we give new results on domain decomposition preconditioners for GMRES when computing piecewise linear finite-element approximations of the Helmholtz equation -\Delta u - (k^2+ \textup {i} \varepsilon )u...

Absorption | Iterative solvers | GMRES | Helmholtz equation | High frequency | Domain decomposition | Preconditioning | MATHEMATICS, APPLIED | high frequency | absorption | domain decomposition | iterative solvers | CONVERGENCE | ALGORITHMS | EQUATION | preconditioning | OPTIMIZED SCHWARZ METHODS

Absorption | Iterative solvers | GMRES | Helmholtz equation | High frequency | Domain decomposition | Preconditioning | MATHEMATICS, APPLIED | high frequency | absorption | domain decomposition | iterative solvers | CONVERGENCE | ALGORITHMS | EQUATION | preconditioning | OPTIMIZED SCHWARZ METHODS

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 10/2015, Volume 295, pp. 127 - 149

.... The proper generalized decomposition (PGD) model reduction approach is used to obtain a separable representation of the solution at any point and for any...

Helmholtz | Proper generalized decomposition | Wave propagation | Reduced order models | Harbor | Parameterized solutions | COMPLEX FLUIDS | BOUNDARY-CONDITIONS | SCATTERING PROBLEMS | METHOD NEFEM | SEPARATED REPRESENTATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | INTERPOLATION METHOD | PARTIAL-DIFFERENTIAL-EQUATIONS | PERFECTLY MATCHED LAYER | MODEL-REDUCTION | FINITE-ELEMENT-METHOD | Harbors | Numerical methods and algorithms | Mètodes numèrics | Classificació AMS | 65 Numerical analysis | Anàlisi numèrica | Matemàtiques i estadística | 65E05 Numerical methods in complex analysis (potential theory, etc.) | Àrees temàtiques de la UPC

Helmholtz | Proper generalized decomposition | Wave propagation | Reduced order models | Harbor | Parameterized solutions | COMPLEX FLUIDS | BOUNDARY-CONDITIONS | SCATTERING PROBLEMS | METHOD NEFEM | SEPARATED REPRESENTATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | INTERPOLATION METHOD | PARTIAL-DIFFERENTIAL-EQUATIONS | PERFECTLY MATCHED LAYER | MODEL-REDUCTION | FINITE-ELEMENT-METHOD | Harbors | Numerical methods and algorithms | Mètodes numèrics | Classificació AMS | 65 Numerical analysis | Anàlisi numèrica | Matemàtiques i estadística | 65E05 Numerical methods in complex analysis (potential theory, etc.) | Àrees temàtiques de la UPC

Journal Article

Journal of geophysics and engineering, ISSN 1742-2140, 2019, Volume 16, Issue 3, pp. 509 - 524

.... This paper envisages the advanced features of a vector-wavefield decomposition method that presents either the P...

DOMAIN | imaging condition | HETEROGENEOUS MEDIA | DEPTH MIGRATION | elastic RTM | EXTRAPOLATION | GEOCHEMISTRY & GEOPHYSICS | PRESTACK | Helmholtz decomposition | S-WAVES | reverse-time migration | PROPAGATION | vector-wavefield decomposition

DOMAIN | imaging condition | HETEROGENEOUS MEDIA | DEPTH MIGRATION | elastic RTM | EXTRAPOLATION | GEOCHEMISTRY & GEOPHYSICS | PRESTACK | Helmholtz decomposition | S-WAVES | reverse-time migration | PROPAGATION | vector-wavefield decomposition

Journal Article

International Journal for Numerical Methods in Engineering, ISSN 0029-5981, 07/2016, Volume 107, Issue 1, pp. 74 - 90

Summary A new and efficient two‐level, non‐overlapping domain decomposition (DD) method is developed for the Helmholtz equation in the two Lagrange multiplier framework...

Helmholtz equation | coarse spaces | non‐overlapping | absorbing interface condition | domain decomposition | preconditioning | non-overlapping | ACOUSTIC SCATTERING | ALGORITHM | LAGRANGE MULTIPLIERS | ITERATIVE SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | PRECONDITIONER | EQUATION | ABSORBING BOUNDARY-CONDITIONS | OPTIMIZED SCHWARZ METHODS | Augmentation | Approximation | Plane waves | Polynomials | Boundaries | Arrays | Optimization | Convergence

Helmholtz equation | coarse spaces | non‐overlapping | absorbing interface condition | domain decomposition | preconditioning | non-overlapping | ACOUSTIC SCATTERING | ALGORITHM | LAGRANGE MULTIPLIERS | ITERATIVE SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | PRECONDITIONER | EQUATION | ABSORBING BOUNDARY-CONDITIONS | OPTIMIZED SCHWARZ METHODS | Augmentation | Approximation | Plane waves | Polynomials | Boundaries | Arrays | Optimization | Convergence

Journal Article

IEEE Transactions on Visualization and Computer Graphics, ISSN 1077-2626, 08/2013, Volume 19, Issue 8, pp. 1386 - 1404

The Helmholtz-Hodge Decomposition (HHD) describes the decomposition of a flow field into its divergence-free and curl-free components...

Visualization | incompressibility | Conferences | Communities | Vector fields | Boundary conditions | Vectors | Physics | Helmholtz-Hodge decomposition | boundary conditions | TOMOGRAPHIC RECONSTRUCTION | THEOREM | ANIMATION | EQUATIONS | VECTOR-FIELDS | FORMULATION | FLOW | COMPUTER SCIENCE, SOFTWARE ENGINEERING | DIVERGENCE-FREE | SCHEME | 2ND-ORDER PROJECTION METHOD

Visualization | incompressibility | Conferences | Communities | Vector fields | Boundary conditions | Vectors | Physics | Helmholtz-Hodge decomposition | boundary conditions | TOMOGRAPHIC RECONSTRUCTION | THEOREM | ANIMATION | EQUATIONS | VECTOR-FIELDS | FORMULATION | FLOW | COMPUTER SCIENCE, SOFTWARE ENGINEERING | DIVERGENCE-FREE | SCHEME | 2ND-ORDER PROJECTION METHOD

Journal Article

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A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation

Journal of computational physics, ISSN 0021-9991, 2012, Volume 231, Issue 2, pp. 262 - 280

This paper presents a new non-overlapping domain decomposition method for the Helmholtz equation, whose effective convergence is quasi-optimal...

Helmholtz equation | Domain decomposition methods | Finite elements | Padé approximants | BOUNDARY-CONDITIONS | LAGRANGE MULTIPLIERS | INTEGRAL-EQUATIONS | Pade approximants | ITERATIVE SOLUTION | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | WAVE-LIKE EQUATIONS | PERFECTLY MATCHED LAYER | HIGH-FREQUENCY | ACOUSTIC SCATTERING PROBLEMS | FINITE-ELEMENT-METHOD | Finite element method | Algorithms | Helmholtz equations | Approximation | Mathematical analysis | Dirichlet problem | Domain decomposition | Convergence | Three dimensional

Helmholtz equation | Domain decomposition methods | Finite elements | Padé approximants | BOUNDARY-CONDITIONS | LAGRANGE MULTIPLIERS | INTEGRAL-EQUATIONS | Pade approximants | ITERATIVE SOLUTION | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | WAVE-LIKE EQUATIONS | PERFECTLY MATCHED LAYER | HIGH-FREQUENCY | ACOUSTIC SCATTERING PROBLEMS | FINITE-ELEMENT-METHOD | Finite element method | Algorithms | Helmholtz equations | Approximation | Mathematical analysis | Dirichlet problem | Domain decomposition | Convergence | Three dimensional

Journal Article

Journal of Mathematical Fluid Mechanics, ISSN 1422-6928, 9/2018, Volume 20, Issue 3, pp. 1093 - 1121

We prove the existence of the Helmholtz decomposition $$ L^q(\Omega _{\mathrm {p}},\mathbb {C}^d)=L_\sigma ^q(\Omega _{\mathrm {p}})\oplus G^q(\Omega _{\mathrm {p}})$$ Lq(Ωp,Cd)=Lσq(Ωp)⊕Gq(Ωp) for periodic domains...

Mathematical Methods in Physics | Fluid- and Aerodynamics | Classical and Continuum Physics | Physics

Mathematical Methods in Physics | Fluid- and Aerodynamics | Classical and Continuum Physics | Physics

Journal Article

International journal for numerical methods in engineering, ISSN 0029-5981, 2017, Volume 109, Issue 8, pp. 1085 - 1102

Summary The identification of the geological structure from seismic data is formulated as an inverse problem. The properties and the shape of the rock...

parameterized Helmholtz problem | seismic analysis | proper generalized decomposition (PGD) | inverse problems | parameter identification | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | EVOLUTION | ENGINEERING, MULTIDISCIPLINARY | OPTIMIZATION | Helmholtz equations | Parameters | Algorithms | Inverse problems | Geophysics | Mathematical models | Decomposition | Parameter identification | Sismologia | Geotècnia | Enginyeria civil | Seismology | Matemàtica | Mathematics | Àrees temàtiques de la UPC

parameterized Helmholtz problem | seismic analysis | proper generalized decomposition (PGD) | inverse problems | parameter identification | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | EVOLUTION | ENGINEERING, MULTIDISCIPLINARY | OPTIMIZATION | Helmholtz equations | Parameters | Algorithms | Inverse problems | Geophysics | Mathematical models | Decomposition | Parameter identification | Sismologia | Geotècnia | Enginyeria civil | Seismology | Matemàtica | Mathematics | Àrees temàtiques de la UPC

Journal Article

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A SOURCE TRANSFER DOMAIN DECOMPOSITION METHOD FOR HELMHOLTZ EQUATIONS IN UNBOUNDED DOMAIN

SIAM journal on numerical analysis, ISSN 0036-1429, 1/2013, Volume 51, Issue 4, pp. 2331 - 2356

We propose and study a domain decomposition method for solving the truncated perfectly matched layer (PML...

Mathematical domains | Mathematical problems | Interpolation | Approximation | Decomposition methods | Acoustic scattering | Coordinate systems | Computational mathematics | Mathematics | Greens function | Helmholtz equation | Source transfer | High frequency waves | PML | MATHEMATICS, APPLIED | CARTESIAN PML APPROXIMATION | PERFECTLY MATCHED LAYER | high frequency waves | source transfer | ACOUSTIC SCATTERING PROBLEMS | Helmholtz equations | Wavelengths | Mathematical analysis | Domain decomposition methods | Constants | Mathematical models | Convergence

Mathematical domains | Mathematical problems | Interpolation | Approximation | Decomposition methods | Acoustic scattering | Coordinate systems | Computational mathematics | Mathematics | Greens function | Helmholtz equation | Source transfer | High frequency waves | PML | MATHEMATICS, APPLIED | CARTESIAN PML APPROXIMATION | PERFECTLY MATCHED LAYER | high frequency waves | source transfer | ACOUSTIC SCATTERING PROBLEMS | Helmholtz equations | Wavelengths | Mathematical analysis | Domain decomposition methods | Constants | Mathematical models | Convergence

Journal Article

Journal of computational physics, ISSN 0021-9991, 2020, Volume 403, p. 109052

....•Developed a high-order algorithm using decomposition framework and FEM-BEM coupling.•Demonstration of FEM-BEM wave simulation in complex heterogeneous and unbounded media...

Heterogeneous | Finite/boundary element methods | Wave propagation | Unbounded | HIGH-ORDER ALGORITHM | CONVERGENCE ANALYSIS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | HELMHOLTZ-EQUATION | BEM-FEM | DEFINITE | PHYSICS, MATHEMATICAL | SCATTERING | Helmholtz equations | Propagation | Computer simulation | Acoustic propagation | Refractivity | Electromagnetic radiation | Two dimensional models | Decomposition | Model accuracy | Free boundaries | Finite element method | Algorithms | Equivalence | Mathematical analysis | Smooth boundaries | Mathematical models

Heterogeneous | Finite/boundary element methods | Wave propagation | Unbounded | HIGH-ORDER ALGORITHM | CONVERGENCE ANALYSIS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | HELMHOLTZ-EQUATION | BEM-FEM | DEFINITE | PHYSICS, MATHEMATICAL | SCATTERING | Helmholtz equations | Propagation | Computer simulation | Acoustic propagation | Refractivity | Electromagnetic radiation | Two dimensional models | Decomposition | Model accuracy | Free boundaries | Finite element method | Algorithms | Equivalence | Mathematical analysis | Smooth boundaries | Mathematical models

Journal Article