| 1. |
- Nordström, Jan, 1953-, et al.
(författare)
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Dual Time-Stepping Using Second Derivatives
- 2019
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Ingår i: Journal of Scientific Computing. - Linköping : Springer. - 0885-7474 .- 1573-7691. ; 81:2, s. 1050-1071
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Tidskriftsartikel (refereegranskat)abstract
- We present a modified formulation of the dual time-stepping technique which makes use of two derivatives in pseudo-time. This new technique retains and improves the convergence properties to the stationary solution. When compared with the conventional dual time-stepping, the method with two derivatives reduces the stiffness of the problem and requires fewer iterations for full convergence to steady-state. In the current formulation, these positive effects require that an approximation of the square root of the spatial operator is available and inexpensive.
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| 2. |
- Ruggiu, Andrea Alessandro, et al.
(författare)
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A new multigrid formulation for high order finite difference methods on summation-by-parts form
- 2017
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Multigrid schemes for high order finite difference methods on summation-by-parts form are studied by comparing the effect of different interpolation operators. By using the standard linear prolongation and restriction operators, the Galerkin condition leads to inaccurate coarse grid discretizations. In this paper, an alternative class of interpolation operators that bypass this issue and preserve the summation-by-parts property on each grid level is considered. Clear improvements of the convergence rate for relevant model problems are achieved.
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| 3. |
- Ruggiu, Andrea Alessandro, et al.
(författare)
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Eigenvalue analysis for summation-by-parts finite difference time discretizations
- 2019
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Diagonal norm finite-difference based time integration methods in summation-by-parts form are investigated. The second, fourth and sixth order accurate discretizations are proven to have eigenvalues with strictly positive real parts. This leads to provably invertible fully-discrete approximations of initial boundary value problems.Our findings also allow us to conclude that the second, fourth and sixth order time discretizations are stiffly accurate, strongly S-stable and dissipatively stable Runge-Kutta methods. The procedure outlined in this article can be extended to even higher order summation-by-parts approximations with repeating stencil.
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