Optimal local truncation error method for solution of elasticity problems for heterogeneous materials with irregular interfaces and unfitted Cartesian meshes

2021 ◽  
pp. 1-17
Author(s):  
A. Idesman ◽  
B. Dey ◽  
M. Mobin
Keyword(s):  
Truncation Error ◽  
Heterogeneous Materials ◽  
Local Truncation Error ◽  
Cartesian Meshes ◽  
Elasticity Problems ◽  
Error Method

ACCURATE FINITE DIFFERENCE REPRESENTATION OF NEUMANN BOUNDARY DATA FOR TIME-HARMONIC WAVE PROPAGATION

1996 ◽  
Vol 04 (04) ◽  
pp. 425-432 ◽  
Author(s):  
ISAAC HARARI
Keyword(s):  
Finite Difference ◽  
Boundary Data ◽  
Truncation Error ◽  
Harmonic Wave ◽  
Neumann Boundary ◽  
Local Truncation Error ◽  
Matrix Equations ◽  
Order Accuracy ◽  
Time Harmonic ◽  
Global Accuracy

Finite difference stencils for inhomogeneous Neumann boundary conditions in acoustic problems with arbitrary source distributions are constructed and analyzed. Boundary stencils are compatible with corresponding interior stencils, preserving symmetry of matrix equations without degrading global accuracy. Higher-order accuracy is attained within the compact support of lower-order methods. Results are verified by local truncation error analysis.

A Loading Correction Scheme for a Structure-Dependent Integration Method

2016 ◽  
Vol 12 (1) ◽  
Author(s):  
Shuenn-Yih Chang
Keyword(s):  
Steady State ◽  
High Frequency ◽  
Truncation Error ◽  
Integration Method ◽  
Frequency Mode ◽  
Local Truncation Error ◽  
Steady State Response ◽  
High Frequency Mode ◽  
State Response ◽  
Correction Scheme

A structure-dependent integration method may experience an unusual overshooting behavior in the steady-state response of a high frequency mode. In order to explore this unusual overshooting behavior, a local truncation error is established from a forced vibration response rather than a free vibration response. As a result, this local truncation error can reveal the root cause of the inaccurate integration of the steady-state response of a high frequency mode. In addition, it generates a loading correction scheme to overcome this unusual overshooting behavior by means of the adjustment the difference equation for displacement. Apparently, these analytical results are applicable to a general structure-dependent integration method.

scholarly journals A Phase-Fitted and Amplification-Fitted Explicit Runge–Kutta–Nyström Pair for Oscillating Systems

2021 ◽  
Vol 26 (3) ◽  
pp. 59
Author(s):  
Musa Ahmed Demba ◽  
Higinio Ramos ◽  
Poom Kumam ◽  
Wiboonsak Watthayu
Keyword(s):  
Stability Analysis ◽  
Numerical Experiments ◽  
Order Of Convergence ◽  
Truncation Error ◽  
Local Truncation Error ◽  
Nyström Methods ◽  
Oscillating Systems ◽  
The Common ◽  
Runge Kutta ◽  
The Stability

An optimized embedded 5(3) pair of explicit Runge–Kutta–Nyström methods with four stages using phase-fitted and amplification-fitted techniques is developed in this paper. The new adapted pair can exactly integrate (except round-off errors) the common test: y″=−w2y. The local truncation error of the new method is derived, and we show that the order of convergence is maintained. The stability analysis is addressed, and we demonstrate that the developed method is absolutely stable, and thus appropriate for solving stiff problems. The numerical experiments show a better performance of the new embedded pair in comparison with other existing RKN pairs of similar characteristics.

scholarly journals Local Truncation Error-Informed Code Verification

2020 ◽  
Vol 5 (4) ◽  
Author(s):  
Aaron M. Krueger ◽  
Vincent A. Mousseau ◽  
Yassin A. Hassan
Keyword(s):  
Numerical Method ◽  
Truncation Error ◽  
Fluid Dynamic ◽  
Local Truncation Error ◽  
Code Verification ◽  
Verification Method ◽  
First Order ◽  
Manufactured Solutions ◽  
Equation Analysis ◽  
Modified Equation

Abstract The method of manufactured solutions (MMS) has become increasingly popular in conducting code verification studies on predictive codes, such as nuclear power system codes and computational fluid dynamic codes. The reason for the popularity of this approach is that it can be used when an analytical solution is not available. Using MMS, code developers are able to verify that their code is free of coding errors that impact the observed order of accuracy. While MMS is still an excellent tool for code verification, it does not identify coding errors that are of the same order as the numerical method. This paper presents a method that combines MMS with modified equation analysis (MEA), which calculates the local truncation error (LTE) to identify coding error up to and including the order of the numerical method. This method is referred to as modified equation analysis methd of manufactured solutions (MEAMMS). MEAMMS is then applied to a custom-built code, which solves the shallow water equations, to test the performance of the code verification method. MEAMMS is able to detect all coding errors that impact the implementation of the numerical scheme. To show how MEAMMS is different than MMS, they are both applied to the same first-order numerical method test problem with a first-order coding error. When there are first-order coding errors, only MEAMMS is able to identify them. This shows that MEAMMS is able to identify a larger set of coding errors while still being able to identify the coding errors MMS is able to identify.

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