Heiner Igel
- Published in print:
- 2016
- Published Online:
- January 2017
- ISBN:
- 9780198717409
- eISBN:
- 9780191835070
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198717409.003.0007
- Subject:
- Physics, Geophysics, Atmospheric and Environmental Physics
The spectral-element method is introduced as a finite-element method with high-order Lagrange polynomials as interpolating functions. The concept of numerical integration is introduced and the ...
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The spectral-element method is introduced as a finite-element method with high-order Lagrange polynomials as interpolating functions. The concept of numerical integration is introduced and the Gauss–Lobatto–Legendre approach is presented as a way to obtain a diagonal mass matrix. The calculation of the mass and stiffness matrices is presented first at an elemental level. The synthesis of the global system of equations is discussed with the result that the diagonal mass matrix allows for a fully explicit time-extrapolation scheme. The method is presented with examples of wave propagation in homogeneous and heterogeneous media.Less
The spectral-element method is introduced as a finite-element method with high-order Lagrange polynomials as interpolating functions. The concept of numerical integration is introduced and the Gauss–Lobatto–Legendre approach is presented as a way to obtain a diagonal mass matrix. The calculation of the mass and stiffness matrices is presented first at an elemental level. The synthesis of the global system of equations is discussed with the result that the diagonal mass matrix allows for a fully explicit time-extrapolation scheme. The method is presented with examples of wave propagation in homogeneous and heterogeneous media.
Heiner Igel
- Published in print:
- 2016
- Published Online:
- January 2017
- ISBN:
- 9780198717409
- eISBN:
- 9780191835070
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198717409.003.0009
- Subject:
- Physics, Geophysics, Atmospheric and Environmental Physics
The discontinuous Galerkin method is introduced as a special type of finite-element method in which the solution fields are allowed to be discontinuous at the element boundaries. This requires the ...
More
The discontinuous Galerkin method is introduced as a special type of finite-element method in which the solution fields are allowed to be discontinuous at the element boundaries. This requires the use of the same fluxes as introduced in the chapter on the finite-volume method. The solution field is interpolated using Lagrange polynomials. The discontinuous Galerkin principle leads to an elemental system of equations. Communication between elements is possible through the fluxes. The method is presented for scalar and elastic wave equations for both homogeneous and heterogeneous media. The method can be considered a mixture of the spectral-element and the finite-volume methods.Less
The discontinuous Galerkin method is introduced as a special type of finite-element method in which the solution fields are allowed to be discontinuous at the element boundaries. This requires the use of the same fluxes as introduced in the chapter on the finite-volume method. The solution field is interpolated using Lagrange polynomials. The discontinuous Galerkin principle leads to an elemental system of equations. Communication between elements is possible through the fluxes. The method is presented for scalar and elastic wave equations for both homogeneous and heterogeneous media. The method can be considered a mixture of the spectral-element and the finite-volume methods.
