DGTD method on curvilinear tetrahedral meshes
Results.DGTDCurvi History
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%center% Scattering cross-section of a gold nanosphere obtained with P'_2_' and P'_3_' interpolation of the EM filed compenents, using affine (linear) and curvilinear meshes with various refinement levels
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%center% Scattering cross-section of a gold nanosphere obtained with P'_2_' and P'_3_' interpolation of the EM field components, using affine (linear) and curvilinear meshes with various refinement levels
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J. Viquerat and C. Scheid\\
A 3D curvilinear discontinuous Galerkin time-domain solver for nanoscale light–matter interactions\\
%newwin% [[http://dx.doi.org/10.1016/j.cam.2015.03.028 | J. Comput. Appl. Math., Vol. 289, pp. 35-70 (2015)]]\\
J. Viquerat and C. Scheid\\
A 3D curvilinear discontinuous Galerkin time-domain solver for nanoscale light–matter interactions\\
%newwin% [[http://dx.doi.org/10.1016/j.cam.2015.03.028 | J. Comput. Appl. Math., Vol. 289, pp. 35-70 (2015)]]\\
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!!!Related publications
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(:title DGTD method on curvilinear tetrahedral meshes:)
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Classical finite element methods rely on tessellations composed of straight-edged elements mapped linearly from a reference element on domains which physical boundaries and interfaces are indifferently straight or curved. This geometrical approximation represents a serious hindrance for high order methods, since it limits the accuracy of the spatial discretization to second order. Thus, exploiting an enhanced representation of the geometrical features of a given electromagnetic wave propagation problem is an important issue in the design of high order methods, such as the Discontinuous Galerkin Time-Domain (DGTD) method. In this study, we exploit a high order mapping for tetrahedra, and focus on specific nanophotonics setups to assess numerically the impact of this modeling improvement in terms of accuracy and performance.
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Classical finite element methods rely on tessellations composed of straight-edged elements mapped linearly from a reference element on domains which physical boundaries and interfaces are indifferently straight or curved. This geometrical approximation represents a serious hindrance for high order methods, since it limits the accuracy of the spatial discretization to second order. Thus, exploiting an enhanced representation of the geometrical features of a given electromagnetic wave propagation problem is an important issue in the design of high order methods, such as the Discontinuous Galerkin Time-Domain (DGTD) method. In this study, we exploit a high order mapping for tetrahedra, and focus on specific nanophotonics setups to assess numerically the gains in terms of accuracy and performance.
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Classical finite element methods rely on tessellations composed of straight-edged elements mapped linearly from a reference element on domains which physical boundaries and interfaces are indifferently straight or curved. This geometrical approximation represents a serious hindrance for high order methods, since it limits the accuracy of the spatial discretization to second order. Thus, exploiting an enhanced representation of the geometrical features of a given electromagnetic wave propagation problem is an important issue in the design of high order methods, such as the Discontinuous Galerkin Time-Domain (DGTD) method. In this study, we exploit a high order mapping for tetrahedra, and focus on specific nanophotonics setups to assess the gains of
to:
Classical finite element methods rely on tessellations composed of straight-edged elements mapped linearly from a reference element on domains which physical boundaries and interfaces are indifferently straight or curved. This geometrical approximation represents a serious hindrance for high order methods, since it limits the accuracy of the spatial discretization to second order. Thus, exploiting an enhanced representation of the geometrical features of a given electromagnetic wave propagation problem is an important issue in the design of high order methods, such as the Discontinuous Galerkin Time-Domain (DGTD) method. In this study, we exploit a high order mapping for tetrahedra, and focus on specific nanophotonics setups to assess numerically the impact of this modeling improvement in terms of accuracy and performance.
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(:cellnr align='center':) Absorption cross-section of a gold nanosphere dimer obtained with P'_4_' approximation using affine and curvilinear meshes
(:cellnr align='center':) Absorption cross-section of a gold nanosphere dimer obtained with P'_4_' approximation using affine and curvilinear meshes
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(:cellnr align='center':) %width=385px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_dimer-cross.png
(:cellnr align='center':) Absorption cross-section of a gold nanosphere dimer obtained with P'_4_' approximation
(:cellnr align='center':) using affine and curvilinear meshes
(:cellnr align='center':) Absorption cross-section of a gold nanosphere dimer obtained with P'_4_' approximation
(:cellnr align='center':) using affine and curvilinear meshes
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(:table border='0' width='100%' align='center' cellspacing='1px':)
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(:cellnr align='center':) Absorption cross-section of a gold nanosphere dimer obtained with P'_4_' approximation using affine and curvilinear meshes
(:tableend:)
(:cellnr align='center':) http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_dimer-cross.png
(:cellnr align='center':) Absorption cross-section of a gold nanosphere dimer obtained with P'_4_' approximation using affine and curvilinear meshes
(:tableend:)
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(:cell align='center':) DGTD method with curvilinear elements
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(:cellnr align='center':) %width=385px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_sphere-cross-cur.png
(:cellnr align='center':) DGTD method with curvilinear elements
(:cellnr align='center':) DGTD method with curvilinear elements
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%lfloat text-align=center width=425px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_dimer-cross.png | Absorption cross-section
of a gold nanosphere dimer obtained with P'_4_' approximation using affine and curvilinear meshes.
of a gold nanosphere dimer obtained with P'_4_' approximation using affine and curvilinear meshes.
to:
%lfloat text-align=center width=425px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_dimer-cross.png | Absorption cross-section of a gold nanosphere dimer obtained with P'_4_' approximation using affine and curvilinear meshes.
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%lfloat text-align=center width=425px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_dimer-cross.png Absorption cross-section
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%lfloat text-align=center width=425px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_dimer-cross.png | Absorption cross-section
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%lfloat text-align=center width=425px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_dimer-cross.png | Absorption cross-section \\
ofa gold nanosphere dimer \\
obtained with P'_4_' approximation using affine and curvilinear meshes.
of
obtained with P'_4_' approximation using affine and curvilinear meshes.
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%lfloat text-align=center width=425px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_dimer-cross.png Absorption cross-section
of a gold nanosphere dimer obtained with P'_4_' approximation using affine and curvilinear meshes.
of a gold nanosphere dimer obtained with P'_4_' approximation using affine and curvilinear meshes.
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%lfloat text-align=center width=425px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_dimer-cross.png | Absorption cross-section of a gold nanosphere dimer obtained with P'_4_' approximation using affine and curvilinear meshes.
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%lfloat text-align=center width=425px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_dimer-cross.png | Absorption cross-section \\
of a gold nanosphere dimer \\
obtained with P'_4_' approximation using affine and curvilinear meshes.
of a gold nanosphere dimer \\
obtained with P'_4_' approximation using affine and curvilinear meshes.
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%lfloat text-align=center width=425px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_dimer-cross.jpg | Absorption cross-section of a gold nanosphere dimer obtained with P'_4_' approximation using affine and curvilinear meshes.
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%lfloat text-align=center width=425px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_dimer-cross.png | Absorption cross-section of a gold nanosphere dimer obtained with P'_4_' approximation using affine and curvilinear meshes.
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%lfloat text-align=center width=375px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_dimer-cross.jpg | Absorption cross-section of a gold nanosphere dimer obtained with P'_4_' approximation using affine and curvilinear meshes.
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%lfloat text-align=center width=425px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_dimer-cross.jpg | Absorption cross-section of a gold nanosphere dimer obtained with P'_4_' approximation using affine and curvilinear meshes.
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%lfloat text-align=center width=300px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_dimer-cross.jpg | Absorption cross-section of a gold nanosphere dimer obtained with P'_4_' approximation using affine
and curvilinear meshes.
and curvilinear meshes.
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%lfloat text-align=center width=375px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_dimer-cross.jpg | Absorption cross-section of a gold nanosphere dimer obtained with P'_4_' approximation using affine and curvilinear meshes.
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%lfloat text-align=center width=300px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_dimer-cross.jpg | Absorption cross-section of a gold nanosphere dimer obtained with P'_4_' approximation using affine
and curvilinear meshes.
and curvilinear meshes.
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%center% Near-field visualization of the electric field Fourier transform for a gold nanosphere dimer
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%center% Near-field visualization of the electric field Fourier transform for a gold nanosphere dimer
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Plasmonic coupling between nanoparticles is at the heart of many applications
in nano-optics. We consider the coupling of two identical gold nanospheres which are aligned along the polarization direction of the incident field, and the surface-to-surface distance is set to 4 nm. In this configuration, the coupled plasmon resonance induces very intense fields in the gap between the particles. Then, a proper near-field resolution is essential to a good understanding of the properties of such coupled structures. To properly account for the high intensity of the fields, we use P4 polynomial approximation with upwind fluxes and a low storage Runge Kutta time-scheme of order 4 (LSRK4).
to:
Plasmonic coupling between nanoparticles is at the heart of many applications in nano-optics. We illustrate the coupling of two identical gold nanospheres which are aligned along the polarization direction of the incident field, and the surface-to-surface distance is set to 4 nm. In this configuration, the coupled plasmon resonance induces very intense fields in the gap between the particles. Then, a proper near-field resolution is essential to a good understanding of the properties of such coupled structures. Here, we use P'_4_' polynomial approximation with upwind fluxes and a fourth order low storage Runge Kutta time scheme (LSRK4).
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Tetrahedral mesh for plasmonic resonance of a gold nanosphere. The scatterer (in red) is enclosed by the total field (TF) region (in blue), delimited by the TF/SF interface on which the incident field is imposed. Then we find the scattered field (SF) region (in purple), surrounded by UPMLs (in gray).
to:
Tetrahedral mesh for plasmonic resonance of a gold nanosphere with radius 50 nm. The scatterer (in red) is enclosed by the total field (TF) region (in blue), delimited by the TF/SF interface on which the incident field is imposed. Then we find the scattered field (SF) region (in purple), surrounded by UPMLs (in gray).
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(:linebreaks:)
Plasmonic coupling between nanoparticles is at the heart of many applications
in nano-optics. We consider the coupling of two identical gold nanospheres which are aligned along the polarization direction of the incident field, and the surface-to-surface distance is set to 4 nm. In this configuration, the coupled plasmon resonance induces very intense fields in the gap between the particles. Then, a proper near-field resolution is essential to a good understanding of the properties of such coupled structures. To properly account for the high intensity of the fields, we use P4 polynomial approximation with upwind fluxes and a low storage Runge Kutta time-scheme of order 4 (LSRK4).
(:linebreaks:)
Plasmonic coupling between nanoparticles is at the heart of many applications
in nano-optics. We consider the coupling of two identical gold nanospheres which are aligned along the polarization direction of the incident field, and the surface-to-surface distance is set to 4 nm. In this configuration, the coupled plasmon resonance induces very intense fields in the gap between the particles. Then, a proper near-field resolution is essential to a good understanding of the properties of such coupled structures. To properly account for the high intensity of the fields, we use P4 polynomial approximation with upwind fluxes and a low storage Runge Kutta time-scheme of order 4 (LSRK4).
(:linebreaks:)
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%center% Near-field visualization of the electric field Fourier transform for a gold nanosphere dimer
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(:cell align='center':) %width=375px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_sphere-cross-cur.jp
(:cellnr align='center':) DGTD method with affine elements
(:cell align='center':) DGTD method with curvilinear elements
(:tableend:)
(:table border='0' width='100%' align='center' cellspacing='1px':)
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(:cellnr align='center':) DGTD method with affine elements
(:cell align='center':) DGTD method with curvilinear elements
(:tableend:)
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%center% Scattering cross-section of a gold nanosphere obtained with P'_2_' and P'_3_' interpolation of the EM filed compenents, using affine (linear)
and curvilinear meshes with various refinementlevels.
and curvilinear meshes with various refinement
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%center% Scattering cross-section of a gold nanosphere obtained with P'_2_' and P'_3_' interpolation of the EM filed compenents, using affine (linear) and curvilinear meshes with various refinement levels
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%center% Scattering cross-section of a gold nanosphere
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%center% Scattering cross-section of a gold nanosphere obtained with P'_2_' and P'_3_' interpolation of the EM filed compenents, using affine (linear)
and curvilinear meshes with various refinement levels.
and curvilinear meshes with various refinement levels.
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%center% Scattering cross-section of a gold nanosphere
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Tetrahedral mesh for plasmonic resonance of a gold nanosphere. The scatterer (in red) is enclosed by the total field (TF) region (in blue), delimited by the TF/SF interface on which the incident field is imposed. Then we find the scattered field (SF) region (in purple), surrounded by UPMLs (in gray).
[[<<]]
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(:cellnr align='center':)[-Local model modulus of Ex component-]
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(:cellnr align='center':) DGTD method with affine elements
(:cell align='center':) DGTD method with curvilinear elements
(:cell align='center':) DGTD method with curvilinear elements
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%lfloat text-align=center width=250px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_sphere-mesh.jpg
Tetrahedral mesh for plasmonic resonance of a gold nanosphere. The scatterer (in red) is enclosed by the total field (TF) region (in blue), delimited by the TF/SF interface on which the incident field is imposed. Then we find the scattered field (SF) region (in purple), surrounded by UPMLs (in gray).
[[<<]]
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(:cell align='center':)[-Non-local model, modulus of Ex component-]
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(:table border='0' width='100%' align='center' cellspacing='1px':)
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(:table border='0' width='500px%' align='center' cellspacing='1px':)
(:cellnr align='center':) %width=200px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_sphere-cross-lin.jpg
(:cell align='center':) %width=200px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_sphere-cross-cur.jpg
(:cellnr align='center':) [-Local model modulus of Ex component-]
(:cell align='center':) [-Non-local model, modulus of Ex component-]
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(:table border='0' width='50%' align='center' cellspacing='1px':)
(:cellnr align='center':)%width=200px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_sphere-cross-lin.jpg
(:cell align='center':)%width=200px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_sphere-cross-cur.jpg
(:cellnr align='center':)[-Local model modulus of Ex component-]
(:cell align='center':)[-Non-local model, modulus of Ex component-]
(:cellnr align='center':)%width=200px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_sphere-cross-lin.jpg
(:cell align='center':)%width=200px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_sphere-cross-cur.jpg
(:cellnr align='center':)[-Local model modulus of Ex component-]
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(:table border='0' width='500px%' align='center' cellspacing='1px':)
(:cellnr align='center':) %width=200px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_sphere-cross-lin.jpg
(:cell align='center':) %width=200px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_sphere-cross-cur.jpg
(:cellnr align='center':) [-Local model modulus of Ex component-]
(:cell align='center':) [-Non-local model, modulus of Ex component-]
(:tableend:)
(:cellnr align='center':) %width=200px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_sphere-cross-lin.jpg
(:cell align='center':) %width=200px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_sphere-cross-cur.jpg
(:cellnr align='center':) [-Local model modulus of Ex component-]
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(:cellnr align='center':) %width=200px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_sphere-cross-lin.jpg
(:cell align='center':) %width=200px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_sphere-cross-cur.jpg
(:cellnr align='center':) [-Local model modulus of Ex component-]
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Tetrahedral mesh for plasmonic resonance of a gold nanosphere. The scatterer (in red) is enclosed by the total field (TF) region (in blue), delimited by the TF/SF interface on which the incident field is imposed. Then we find the scattered field (SF) region (in purple), surrounded by UPMLs (in gray). \\
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Tetrahedral mesh for plasmonic resonance of a gold nanosphere. The scatterer (in red) is enclosed by the total field (TF) region (in blue), delimited by the TF/SF interface on which the incident field is imposed. Then we find the scattered field (SF) region (in purple), surrounded by UPMLs (in gray).
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Tetrahedral mesh for plasmonic resonance of a gold nanosphere. The scatterer (in red) is enclosed by the total field (TF) region (in blue), delimited by the TF/SF interface on which the incident field is imposed. Then we find the scattered field (SF) region (in purple), surrounded by UPMLs (in gray).
to:
Tetrahedral mesh for plasmonic resonance of a gold nanosphere. The scatterer (in red) is enclosed by the total field (TF) region (in blue), delimited by the TF/SF interface on which the incident field is imposed. Then we find the scattered field (SF) region (in purple), surrounded by UPMLs (in gray). \\
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(:cellnr align='center':)%width=200px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_sphere-lin.jpg
(:cell align='center':)%width=200px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_sphere-cur.jpg
(:cellnr align='center':) [-Local model modulus of Ex component-]
(:cell align='center':)%width=200px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_sphere-cur.jpg
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(:cellnr align='center':) %width=200px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_sphere-cross-lin.jpg
(:cell align='center':) %width=200px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_sphere-cross-cur.jpg
(:cellnr align='center':) [-Local model modulus of Ex component-]
(:cell align='center':) %width=200px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_sphere-cross-cur.jpg
(:cellnr align='center':) [-Local model modulus of Ex component-]
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Classical finite element methods rely on tessellations composed of straight-edged elements mapped linearly from a reference element, on domains which physical boundaries and interfaces are indifferently straight or curved. This approximation represents serious hindrance for high-order methods, since it limits the accuracy of the spatial discretization to second order. Thus, exploiting an enhanced representation of the geometrical features of a given electromagnetic wave propagation problem is an important issue in the design of high-order methods, such as the Discontinuous Galerkin Time-Domain (DGTD) method. In the latter framework, we propose and validate an implementation of a high-order mapping for tetrahedra, and then focus on specific nanophotonics setups to assess the gains of the method in terms of memory and performances.
to:
Classical finite element methods rely on tessellations composed of straight-edged elements mapped linearly from a reference element on domains which physical boundaries and interfaces are indifferently straight or curved. This geometrical approximation represents a serious hindrance for high order methods, since it limits the accuracy of the spatial discretization to second order. Thus, exploiting an enhanced representation of the geometrical features of a given electromagnetic wave propagation problem is an important issue in the design of high order methods, such as the Discontinuous Galerkin Time-Domain (DGTD) method. In this study, we exploit a high order mapping for tetrahedra, and focus on specific nanophotonics setups to assess the gains of in terms of accuracy and performance.
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(:cell align='center':)%width=200px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_sphere-cur.jpg
(:cellnr align='center':) [-Local model modulus of Ex component-]
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Classical finite element methods rely on tessellations composed of straight-edged elements mapped linearly from a reference element, on domains which physical boundaries and interfaces are indifferently straight or curved. This approximation represents serious hindrance for high-order methods, since
to:
Classical finite element methods rely on tessellations composed of straight-edged elements mapped linearly from a reference element, on domains which physical boundaries and interfaces are indifferently straight or curved. This approximation represents serious hindrance for high-order methods, since it limits the accuracy of the spatial discretization to second order. Thus, exploiting an enhanced representation of the geometrical features of a given electromagnetic wave propagation problem is an important issue in the design of high-order methods, such as the Discontinuous Galerkin Time-Domain (DGTD) method. In the latter framework, we propose and validate an implementation of a high-order mapping for tetrahedra, and then focus on specific nanophotonics setups to assess the gains of the method in terms of memory and performances.
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Classical finite element methods rely on tessellations composed of straight-edged elements mapped linearly from a reference element, on domains which physical boundaries and interfaces are indifferently straight or curved. This approximation represents serious hindrance for high-order methods, since they limit the precision of the spatial discretization to second order. Thus, exploiting an enhanced representation of the physical geometry of a considered problem is in agreement with the natural procedure of high-order methods, such as the discontinuous Galerkin method. In the latter framework, we propose and validate an implementation of a high-order mapping for tetrahedra, and then focus on specific nanophotonics setups to assess the gains of the method in terms of memory and performances.
%lfloat text-align=center width=250px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_sphere-mesh.jpg
Tetrahedral mesh for plasmonic resonance of a gold nanosphere. The scatterer (in red) is enclosed by the total field (TF) region (in blue), delimited by the TF/SF interface on which the incident field is imposed. Then we find the scattered field (SF) region (in purple), surrounded by UPMLs (in gray).
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%lfloat text-align=center width=250px% http://www-sop.inria.fr/nachos/pics/results/nano_sphere/nano_sphere-mesh.jpg
Tetrahedral mesh for plasmonic resonance of a gold nanosphere. The scatterer (in red) is enclosed by the total field (TF) region (in blue), delimited by the TF/SF interface on which the incident field is imposed. Then we find the scattered field (SF) region (in purple), surrounded by UPMLs (in gray).
[[<<]]