A platform for research: civil engineering, architecture and urbanism
A platform for research: civil engineering, architecture and urbanism
Direct approaches can provide the exact solution of a system of linear equation. Iterative technique reaches to a solution close to the exact solution of the system of linear equation via performing a series of calculations within a loop. Evidently, the closeness of the results needs to be defined by a user based on the nature of a problem and the desired accuracy from a computational fluid dynamics simulation. This chapter discusses each of direct and iterative methods with their associated advantages and disadvantages. Common examples of a direct solution of system of linear algebraic equation include Cramer's rule in matrix inversion, Gaussian elimination, and one‐dimensional tri‐diagonal matrix algorithm. The errors between the current solution and the final solution are known as the iterative convergence error. A logical transformation of a real‐world problem to a correct model implies the validation process.
Direct approaches can provide the exact solution of a system of linear equation. Iterative technique reaches to a solution close to the exact solution of the system of linear equation via performing a series of calculations within a loop. Evidently, the closeness of the results needs to be defined by a user based on the nature of a problem and the desired accuracy from a computational fluid dynamics simulation. This chapter discusses each of direct and iterative methods with their associated advantages and disadvantages. Common examples of a direct solution of system of linear algebraic equation include Cramer's rule in matrix inversion, Gaussian elimination, and one‐dimensional tri‐diagonal matrix algorithm. The errors between the current solution and the final solution are known as the iterative convergence error. A logical transformation of a real‐world problem to a correct model implies the validation process.
Solvers and Solution Analysis
Mirzaei, Parham A. (author)
2022-10-17
44 pages
Article/Chapter (Book)
Electronic Resource
English
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