| 1. |
- Abbas, Qaisar, et al.
(författare)
-
A weak boundary procedure for high order finite difference approximations of hyperbolic problems
- 2011
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We introduce a new weak boundary procedures for high order finite difference operators on summation-by-parts type applied to hyperbolic problems. The boundary procedure is applied in an extended domain where data is known. We show how to raise the order of accuracy for a diagonal norm based approximation and how to modify the spectrum of the resulting operator to get a faster convergence to steady-state. Furthermore, we also show how to construct better non-reflecting properties at the boundaries using the above procedure. Numerical results that corroborate the analysis are presented.
|
|
| 2. |
- Amsallem, David, et al.
(författare)
-
High-order accurate difference schemes for the Hodgkin-Huxley equations
- 2012
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- A novel approach for simulating potential propagation in neuronal branches with high accuracy is developed. The method relies on high-order accurate dierence schemes using the Summation-By-Parts operators with weak boundary and interface conditions applied to the Hodgkin-Huxley equations. This work is the rst demonstrating high accuracy for that equation. Several boundary conditions are considered including the non-standard one accounting for the soma presence, which is characterized by its own partial dierential equation. Well-posedness for the continuous problem as well as stability of the discrete approximation is proved for all the boundary conditions. Gains in terms of CPU times are observed when high-order operators are used, demonstrating the advantage of the high-order schemes for simulating potential propagation in large neuronal trees.
|
|
| 3. |
|
|
| 4. |
|
|
| 5. |
|
|
| 6. |
- Carpenter, Mark H., et al.
(författare)
-
Revisiting and extending interface penalties for multi-domain summation-by-parts operators
- 2009
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- A general interface procedure is presented for multi-domain collocation methods satisfying the summation-by-parts (SBP) spatial discretization convention. Unlike more traditional operators (e.g. FEM) applied to the advection-diffusion equation, the new procedure penalizes the solution and the first p derivatives across the interface. The combined interior/interface operators are proven to be pointwise stable, and conservative, although accuracy deteriorates for p>=2. Penalties between two different sets of variables are compared (motivated by FEM primal and flux formulations), and are shown to be equivalent for certain choices of penalty parameters. Extensive validation studies are presented using two classes of high-order SBP operators: 1) central finite difference, and 2) Legendre spectral collocation.
|
|
| 7. |
- Erickson, Brittany. A., et al.
(författare)
-
Stable, High Order Accurate Adaptive Schemes for Long Time, Highly Intermittent Geophysics Problems
- 2013
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Many geophysical phenomena are characterized by properties that evolve over a wide range of scales which introduce difficulties when attempting to model these features in one computational method. We have developed a high-order finite difference method for the elastic wave equation that is able to efficiently handle varying temporal scales in a single, stand-alone framework. We apply this method to earthquake cycle models characterized by extremely long interseismic periods interspersed with abrupt, short periods of dynamic rupture. Through the use of summation-by-parts operators and weak enforcement of boundary conditions we derive a provably stable discretization. Time stepping is achieved through the implicit θ-method which allows us to take large time steps during the intermittent period between earthquakes and adapts appropriately to fully resolve rupture.
|
|
| 8. |
- Eriksson, Sofia, et al.
(författare)
-
Exact non-reflecting boundary conditions revisited : well-posedness and stability
- 2012
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Exact non-reflecting boundary conditions for an incompletely parabolic system have been studied. It is shown that well-posedness is a fundamental property of the non-reflecting boundary conditions. By using summation by parts operators for the numerical approximation and a weak boundary implementation, energy stability follows automatically. The stability in combination with the high order accuracy results in a reliable, efficient and accurate method. The theory is supported by numerical simulations.
|
|
| 9. |
|
|
| 10. |
- Eriksson, Sofia, et al.
(författare)
-
Simulations of Ground Effects on Wake Vortices at Runways
- 2007
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- n this paper the interaction between two counter-rotating vortices is examined, and the performance of a newly developed finite difference code is discussed. The Reynolds numbers considered are low to medium, and the flow is compressible. Most of the computations are performed in a two dimensional domain, with different grid sizes, Reynolds number and order of accuracy of the scheme. Finally, a three dimensional computation is made in order to examine the relevance of the two dimensional model.
|
|
