Friday, November 10, 2023

🔍📊 Summary of the Code with Emojis for FindRoot.C in SWMM5

 🔍📊 Summary of the Code with Emojis

This code snippet focuses on finding the roots of a function, i.e., solving for func(x) = 0, using two distinct methods: Newton-Raphson method and Ridder's Method. Authored by L. Rossman on 11/19/13, it's a part of a larger numerical analysis routine.

1. Newton-Raphson Method 📐🔢

  • Purpose: Used to find the root of a function bracketed between x1 and x2.
  • Process: Combines Newton-Raphson and bisection methods.
  • Root Refinement: Refines the root rts within an accuracy of +/-xacc.
  • Function Evaluations: Returns the number of evaluations used or 0 if maximum iterations are exceeded.
  • Constraints: Requires that func(x1) and func(x2) have opposite signs.
  • Adjustments: May need to recalibrate subcatchment's properties like Percent Impervious and Width after LID placement.
  • Special Conditions: Handles cases where Green Roofs and Roof Disconnection only treat direct precipitation.

2. Ridder's Method 🧮📉

  • Functionality: Finds the root of func between x1 and x2 within an accuracy of xacc.
  • Return Values: Returns the root if found, or a large negative number if not.
  • Methodology: Uses an algorithmic approach to refine the root estimate.
  • Conditions: Effective when func(x1) and func(x2) have opposite signs.
  • Iterations: Executes up to a maximum of MAXIT iterations.
  • Result: If the method converges, it returns the estimated root value.

Common Aspects of Both Methods 🔍🔄

  • Max Iterations: Both methods limit the number of iterations to MAXIT (60).
  • Accuracy: Aim to refine the root estimate to within a specified accuracy (xacc).
  • Error Checking: Includes checks for function values and bisection requirements.

Implementation Details 🖥️💡

  • Header File: Utilizes a custom header file findroot.h.
  • Mathematical Functions: Employs standard math functions from math.h.
  • Constants: Defines a SIGN function and sets MAXIT as 60.

Application Scenario 🌍📚

This code is typically used in scenarios like hydrological modeling or environmental simulations where root-finding algorithms are crucial for analyzing and predicting natural processes.

🔎 In summary, the code effectively implements two root-finding algorithms with careful considerations for accuracy, iteration limits, and method-specific conditions, making it a valuable tool for numerical computations in various scientific and engineering applications.

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