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This research aims to improve wave equation simulations on curved domains using isogeometric analysis with Python.

Isogeometric Analysis of the Wave Equation on Curved Domains Using Python: B-spline Parameterization, Stability Analysis and Numerical Validation

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Randomized trial demonstrates accurate wave simulations in curved domains, indicating improvements over traditional methods.

This research aims to improve wave equation simulations on curved domains using isogeometric analysis with Python.
Developed a Python implementation of isogeometric analysis for the wave equation on curved geometries.
Constructed B-spline parameterizations of a semicircular membrane and a quarter-annular plate without geometric errors.
Discretized the weak Galerkin formulation using B-splines and a fourth-order Runge-Kutta scheme, integrating a generalized CFL condition.
Achieved optimal convergence rates with quadratic B-splines, observed rate of 2.98, close to theoretical value of 3.
IGA solution for the quarter-annulus had only 0.3% error versus 2.1% error for standard FEM, a sevenfold improvement.
Predicted numerical CFL limit accurately using the generalized condition.

Bah et al. (2026) studied this question.

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