Generalised summation-by-parts operators and variable coefficients
نویسندگان
چکیده
منابع مشابه
Summation by Parts Operators for Finite Difference Approximations of Second-Derivatives with Variable Coefficients
Finite difference operators approximating second derivatives with variable coefficients and satisfying a summation-by-parts rule have been derived for the second-, fourthand sixth-order case by using the symbolic mathematics software Maple. The operators are based on the same norms as the corresponding approximations of the first derivate, which makes the construction of stable approximations t...
متن کاملGeneralized Summation-by-Parts Operators for the Second Derivative with Variable Coefficients
The comprehensive generalization of summation-by-parts of Del Rey Fernández et al. (J. Comput. Phys., 266, 2014) is extended to approximations of second derivatives with variable coefficients. This enables the construction of second-derivative operators with one or more of the following characteristics: i) non-repeating interior stencil, ii) nonuniform nodal distributions, and iii) exclusion of...
متن کاملSummation-by-parts operators and high-order quadrature
Summation-by-parts (SBP) operators are finite-difference operators that mimic integration by parts. The SBP operator definition includes a weight matrix that is used formally for discrete integration; however, the accuracy of the weight matrix as a quadrature rule is not explicitly part of the SBP definition. We show that SBP weight matrices are related to trapezoid rules with end corrections w...
متن کاملOn Coordinate Transformations for Summation-by-Parts Operators
High order finite difference methods obeying a summation-by-parts (SBP) rule are developed for equidistant grids. With curvilinear grids, a coordinate transformation operator that does not destroy the SBP property must be used. We show that it is impossible to construct such an operator without decreasing the order of accuracy of the method.
متن کاملSummation-By-Parts Operators for Time Discretisation: Initial Investigations
We develop a new high order accurate time-discretisation technique for initial value problems. We focus on problems that originate from a space discretisation using high order finite difference methods on summation-by-parts form with weak boundary conditions, and extend that technique to the time-domain. The new timediscretisation method is global and together with the approximation in space, i...
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ژورنال
عنوان ژورنال: Journal of Computational Physics
سال: 2018
ISSN: 0021-9991
DOI: 10.1016/j.jcp.2018.02.021