Energy Conservative Methods for Time-Dependent Problems with Nonlinear and Irregular Boundary Conditions

Isogeometric analysis is a numerical method for solving Maxwell’s equations, which describe the behavior of electromagnetic fields. In this article, we explore how isogeometric analysis can be used to improve the accuracy and efficiency of numerical simulations in various applications, including electromagnetic wave propagation and radiation.
To understand why isogeometric analysis is useful, let’s first consider traditional numerical methods for solving Maxwell’s equations. These methods typically use finite element or finite difference techniques, which involve dividing the problem domain into small elements or cells and approximating the solution using simple shapes or functions. However, these methods can produce inaccurate results when dealing with complex geometries or rapidly changing electromagnetic fields.
Isogeometric analysis avoids these problems by using the same basis functions for both the geometry and the solution. This allows for a more accurate approximation of the solution and can significantly reduce computational costs. In isogeometric analysis, the geometry is represented using B-splines or NURBS (non-uniform rational B-splines), which are flexible and can accurately represent complex shapes. The solution is then approximated using the same basis functions as the geometry, resulting in a more accurate and efficient numerical simulation.
The article presents several examples of how isogeometric analysis has been applied to various problems in electromagnetics, including the simulation of electromagnetic wave propagation in complex geometries and the calculation of radiation patterns from arbitrary shapes. The authors also discuss the theoretical foundations of isogeometric analysis and its relationship to other numerical methods for solving Maxwell’s equations.
Overall, this article demonstrates the potential of isogeometric analysis as a powerful tool for simulating electromagnetic phenomena in complex geometries. By using the same basis functions for both the geometry and the solution, isogeometric analysis can provide more accurate and efficient numerical simulations than traditional methods. As such, it has the potential to significantly advance our understanding of electromagnetic phenomena in a wide range of fields, from optics and photonics to wireless communication and radar.