Sorry to bother you again, and thank you for your previous response. Following your recommendation, I read the literature on the solution of interactions between dislocations under periodic boundary conditions, specifically (2.1.25a) and (2.1.25b). However, due to my limited ability, I still have some doubts:
-
(2.1.25a) and (2.1.25b) describe the situation where both dimensions have periodic boundaries. In your code, it seems that only the Y boundary is periodic, while the X direction is not considered. However, in your later dislocation module regarding dislocation movement, the periodic boundary conditions consider both dimensions.
-
Many papers also apply periodic boundary conditions in just one dimensional direction, so it seems feasible to do so, but it is suggested that only the X direction be considered periodic, as is adopted in most studies.
-
In fact, the formula in the doctoral dissertation 'A new O(N) method for modeling and simulating the behavior of a large number of dislocations' is quite difficult to understand. I found the formula in the paper 'Conditional convergence in two-dimensional dislocation dynamics' relatively easier to comprehend. However, even with this reference, I am not able to correlate it well with the formulas in your code. Could you provide the detailed formulas used in your code for solving under periodic boundary conditions?
-
After searching your articles, I found that you have done many interesting works on dislocation dynamics. In fact, I am just a beginner and look forward to more content in this code in the future. I will continue to follow and learn from you.
Thank you again for sharing!
(2.1.25a) and (2.1.25b) describe the situation where both dimensions have periodic boundaries. In your code, it seems that only the Y boundary is periodic, while the X direction is not considered. However, in your later dislocation module regarding dislocation movement, the periodic boundary conditions consider both dimensions.
Many papers also apply periodic boundary conditions in just one dimensional direction, so it seems feasible to do so, but it is suggested that only the X direction be considered periodic, as is adopted in most studies.
In fact, the formula in the doctoral dissertation 'A new O(N) method for modeling and simulating the behavior of a large number of dislocations' is quite difficult to understand. I found the formula in the paper 'Conditional convergence in two-dimensional dislocation dynamics' relatively easier to comprehend. However, even with this reference, I am not able to correlate it well with the formulas in your code. Could you provide the detailed formulas used in your code for solving under periodic boundary conditions?
After searching your articles, I found that you have done many interesting works on dislocation dynamics. In fact, I am just a beginner and look forward to more content in this code in the future. I will continue to follow and learn from you.
Thank you again for sharing!