Finite Element And Discontinuous Galerkin Methods For Transient Wave Equations (scientific Computation)
by Gary Cohen /
2016 / English / PDF
9.5 MB Download
This monograph presents numerical methods for solving transient
wave equations (i.e. in time domain). More precisely, it provides
an overview of continuous and discontinuous finite element
methods for these equations, including their implementation in
physical models, an extensive description of 2D and 3D elements
with different shapes, such as prisms or pyramids, an analysis of
the accuracy of the methods and the study of the Maxwell’s system
and the important problem of its spurious free approximations.
After recalling the classical models, i.e. acoustics, linear
elastodynamics and electromagnetism and their variational
formulations, the authors present a wide variety of finite
elements of different shapes useful for the numerical resolution
of wave equations. Then, they focus on the construction of
efficient continuous and discontinuous Galerkin methods and study
their accuracy by plane wave techniques and a priori error
estimates. A chapter is devoted to the Maxwell’s system and the
important problem of its spurious-free approximations. Treatment
of unbounded domains by Absorbing Boundary Conditions (ABC) and
Perfectly Matched Layers (PML) is described and analyzed in a
separate chapter. The two last chapters deal with time
approximation including local time-stepping and with the study of
some complex models, i.e. acoustics in flow, gravity waves and
vibrating thin plates. Throughout, emphasis is put on the
accuracy and computational efficiency of the methods, with
attention brought to their practical aspects.
This monograph presents numerical methods for solving transient
wave equations (i.e. in time domain). More precisely, it provides
an overview of continuous and discontinuous finite element
methods for these equations, including their implementation in
physical models, an extensive description of 2D and 3D elements
with different shapes, such as prisms or pyramids, an analysis of
the accuracy of the methods and the study of the Maxwell’s system
and the important problem of its spurious free approximations.
After recalling the classical models, i.e. acoustics, linear
elastodynamics and electromagnetism and their variational
formulations, the authors present a wide variety of finite
elements of different shapes useful for the numerical resolution
of wave equations. Then, they focus on the construction of
efficient continuous and discontinuous Galerkin methods and study
their accuracy by plane wave techniques and a priori error
estimates. A chapter is devoted to the Maxwell’s system and the
important problem of its spurious-free approximations. Treatment
of unbounded domains by Absorbing Boundary Conditions (ABC) and
Perfectly Matched Layers (PML) is described and analyzed in a
separate chapter. The two last chapters deal with time
approximation including local time-stepping and with the study of
some complex models, i.e. acoustics in flow, gravity waves and
vibrating thin plates. Throughout, emphasis is put on the
accuracy and computational efficiency of the methods, with
attention brought to their practical aspects.
This monograph also covers in details the theoretical foundations
and numerical analysis of these methods. As a result, this
monograph will be of interest to practitioners, researchers,
engineers and graduate students involved in the numerical
simulation
This monograph also covers in details the theoretical foundations
and numerical analysis of these methods. As a result, this
monograph will be of interest to practitioners, researchers,
engineers and graduate students involved in the numerical
simulation
of waves.
of waves.
