Name
Title | ||
|---|---|---|
Optimized explicit finite-difference schemes for spatial derivatives using maximum norm |
Abstract | ||
|---|---|---|
We propose an optimized scheme using the maximum norm and the simulated annealing.The maximum norm offers the largest set of possible solutions for solvers to search.The explicit finite-difference operator is greatly improved by our optimized scheme.We use a tight error limitation to make accuracy improvement to be high and solid.Our optimized scheme allows greater saving of computational cost and memory demand. Conventional explicit finite-difference methods have difficulties in handling high-frequency components due to strong numerical dispersions. One can reduce the numerical dispersions by optimizing the constant coefficients of the finite-difference operator. Different from traditional optimized schemes that use the 2-norm and the least squares, we propose to construct the objective functions using the maximum norm and solve the objective functions using the simulated annealing algorithm. Both theoretical analyses and numerical experiments show that our optimized scheme is superior to traditional optimized schemes with regard to the following three aspects. First, it provides us with much more flexibility when designing the objective functions; thus we can use various possible forms and contents to make the objective functions more reasonable. Second, it allows for tighter error limitation, which is shown to be necessary to avoid rapid error accumulations for simulations on large-scale models with long travel times. Finally, it is powerful to obtain the optimized coefficients that are much closer to the theoretical limits, which means greater savings in computational efforts and memory demand. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1016/j.jcp.2013.04.029 | J. Comput. Physics |
Keywords | Field | DocType |
numerical experiment,strong numerical dispersion,optimized coefficient,finite-difference operator,objective function,conventional explicit finite-difference method,optimized scheme,numerical dispersion,optimized explicit finite-difference scheme,rapid error accumulation,traditional optimized scheme,maximum norm,spatial derivative,simulated annealing algorithm | Simulated annealing,Least squares,Mathematical optimization,Finite difference,Constant coefficients,Operator (computer programming),Numerical dispersion,Mathematics | Journal |
Volume | Issue | ISSN |
250 | C | 0021-9991 |
Citations | PageRank | References |
12 | 1.17 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jinhai Zhang | 1 | 17 | 3.41 |
| Yao Zhenxing | 2 | 19 | 4.03 |