One-Way Wave Solvers

• Features:
  • Upwind, central, and third-order spatial discretizations, to be combined with forward (theta=0), backward (theta=1), and Crank-Nicolson (theta=0.5) time-discretizations.
  • Lax-Friedrichs and LeapFrog schemes.
  • The first-, second-, and third-order ENO schemes (ENO1,DNO2, ENO3) and a second-order Lax-Friedrichs scheme.
  • The diffusion coefficient (epsilon) is run-time adjustable, along with the wave velocity (vel).
  • Language: C++, C, and F77
• Source code & Documentation: Wave1D.CF.tar
• Note: It fits well with an early-stage project for students in Numerical PDE classes.

Acoustic Waves in 2D

• Features:
  • Equation: Time-domain Acoustics with general velocities.
  • Domain: Rectangle
  • Mesh: Uniform
  • Second-order in both temporal and spatial directions.
  • Explicit and Explicit.
  • Language: C++, C, and F77
• Source code & Documentation: Acoustic2D.CF.tar
• Note: It is from a joint work with Dr. Jim Douglas, Jr., Purdue University, and Hyeona Lim, Michigan State University.

LOD: Microscale Heat Transfer in 2D

• Features:
  • Equation: The microscale heat wave equation
  • Domain: Rectangle
  • Mesh: Uniform
  • Discretizer: The Crank-Nicolson and the central FD.
  • The elliptic solver: LOD
  • Language: C++, C, and F77
• Source code & Documentation: Heat_Micro.CF.tar

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CGNR for Helmholtz Wave Equation in 2D

• Features:
  • Equation: The Helmholtz wave equation in 2D of general, large wave numbers
  • Domain: Rectangle
  • Mesh: Uniform
  • Discretizer: 9-point compact scheme
  • Language: C++, C, and F77
• Source code & Documentation: CGNR_Helm.CF.tar

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MultiGrid method for Helmholtz Equation in 2D

• Features:
  • Equation: The Helmholtz wave equation in 2D of general, large wave numbers
  • Domain: Rectangle
  • Mesh: Uniform
  • Discretizer: the central finite difference
  • Methods: Multigrid and domain decomposition methods
  • Language: C++, C, and F77
• Source code & Documentation: MG_Helm2D_01.CF.tar and MG_Helm_Comp.ps (to appear in SIAM J. Sci. Comput.)
  Also see: S. Kim, Domain decomposition iterative procedures for solving scalar waves in the frequency domain, Numer. Math. 79, 1998, pp.231-259.

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Helmholtz Wave Solver in 3D

• Features:
  • Equation: The Helmholtz wave equation in 3D of general, large wave numbers
  • Domain: Rectangle
  • Mesh: Uniform
  • Discretizer: the central finite difference
  • Methods: CGNR (Conjugate Gradient applied to the normal equation)
  • Language: F77
• Source code & Documentation: 3D_Helm_CGNR.F.tar

Prestack Kirchhoff Depth Migration in 2D and 3D

• Features:
  • Operation: Reflector inversion in 2D and 3D.
  • Language: Mainly F77, and C for IO routines
  • Note: The 2D code was implemented by Prof. Bill Symes, Rice University, and I implemented the 3D code as an extension of the 2D code.
• Source code & Documentation: Kirch_Mig.F.tar

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