In this paper, we consider the parameter identification problem of partial differential equations with constraints. A nonlinear multigrid method is introduced to the process of parameter inversion. By keeping the objective functions on coarse grids c...
In the article, we propose a combination method based on the multigrid method and constraint data to solve the inverse problem in the context of the nonlinear convection–diffusion equation in the multiphase porous media flow. The inverse proble...
This paper delves into a rapid and accurate numerical solution for the inverse problem of the nonlinear diffusion equation in the context of multiphase porous media flow. For the realization of this, the combination of the multigrid method with const...
A high-order compact (HOC) implicit difference scheme is proposed for solving three-dimensional (3D) unsteady reaction diffusion equations. To discretize the spatial second-order derivatives, the fourth-order compact difference operators are used, an...
We present a nonlinear multigrid implementation for the two-dimensional Cahn–Hilliard (CH) equation and conduct detailed numerical tests to explore the performance of the multigrid method for the CH equation. The CH equation was originally deve...
This paper proposes a fast multigrid algorithm to simulate the non-linear motion of ships in both intact and damaged conditions. The simulations of ship motions in waves are known to require much time to calculate due to the strong non-linear interac...
In this study, a class of nonlinear heterogeneous reaction–diffusion system (RDS) has been considered that arises in modeling epidemiological interactions, environmental sciences, and chemical and ecological systems. Numerical and analytic solu...
Convection in a partitioned porous layer is considered where the thin partition causes a mechanical isolation of the two identical sublayers from one another, but heat may neveretheless conduct freely. An unsteady solver that employs the multigrid me...
For the safe and efficient operation of dams, frequent monitoring and maintenance are required. These are usually expensive, time consuming, and cumbersome. To alleviate these issues, we propose applying a wave-based scheme for the location and quant...
This paper investigates co-continuous structures in immiscible polymer blends through three-dimensional (3D) computational calculations based on a multiphase phase-field equation for fluid flow. The mathematical model describes phase separation with...
Cylindrical roller bearings are widely used in industrial machinery, automotive systems, and aerospace applications, where their reliability directly affects the performance and safety of mechanical systems. The fatigue life of cylindrical roller bea...