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A DOMAIN DECOMPOSITION PRECONDITIONING FOR AN INVERSE VOLUME SCATTERING PROBLEM.

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We developed new domain decomposition preconditioners to speed up solving acoustic scattering problems. These methods accelerate iterative solvers for both forward and inverse scattering, improving computational efficiency.

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Area of Science:

  • Computational mathematics
  • Acoustics
  • Numerical analysis

Background:

  • Integral equation formulations are crucial for acoustic scattering problems.
  • Iterative solvers often require acceleration techniques for efficiency.
  • Domain decomposition methods are effective for partial differential equations.

Purpose of the Study:

  • To propose novel domain decomposition preconditioners for acoustic forward and inverse scattering problems.
  • To accelerate iterative solvers used in integral equation formulations.
  • To enhance the efficiency of computational methods for scattering phenomena.

Main Methods:

  • Extending domain decomposition preconditioning techniques from PDEs to integral equations.
  • Combining domain decomposition with low-rank corrections for forward scattering.
  • Utilizing forward problem preconditioners to build inverse problem preconditioners (Gauss-Newton Hessian).

Main Results:

  • Demonstrated the effectiveness of the proposed domain decomposition preconditioners.
  • Showcased accelerated convergence for iterative solvers in acoustic scattering.
  • Validated the performance of combined domain decomposition and low-rank correction strategies.

Conclusions:

  • Domain decomposition preconditioners significantly enhance the solution of integral equations for acoustic scattering.
  • The proposed methods offer efficient computational strategies for both forward and inverse scattering problems.
  • This work provides a foundation for advanced numerical techniques in wave propagation and inverse problems.