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A fast element-free Galerkin (EFG) method is proposed in this paper for solving the nonlinear complex Ginzburg–Landau equation. A second-order accurate time semi-discrete system is presented by using the Crank–Nicolson scheme for the temporal ...

In this paper, the space-time generalized finite difference scheme is applied to solve the nonlinear high-order Korteweg-de Vries equations in multiple dimensions. The proposed numerical scheme combines the space-time generalized finite ...

In this paper the three-dimensional extension of the Diffused Vortex Hydrodynamics (DVH) is discussed along with free vorticity dynamics simulations. DVH is a vortex particle method developed in-house and widely validated in a 2D framework. The ...

The stabilized collocation method (SCM) is a promising meshless collocation method that can overcome the instability defects in the classical direct collocation method. To improve the performance of the SCM, a superconvergent stabilized ...

• A superconvergent stabilized collocation method is developed for linear and nonlinear elliptic problems.
• Theoretical accuracy of the method is analyzed detailedly.
• Theoretical and numerical results reveal that the method possesses ...

In this paper, a fast element-free Galerkin (EFG) method is proposed for solving the multi-term time-fractional diffusion equation (TFDE). Through the use of the multi-term L 2 − 1 σ formula to discrete the multi-term Caputo time-fractional ...

A boundary point interpolation method (BPIM) is presented in this paper for numerical solving acoustic problems. The BPIM is a boundary-type meshless method that combines the point interpolation technique for constructing approximate functions ...

• An efficient BIEs-based method is presented for meshless analysis of acoustic problems.
• Clenshaw-Curtis integration technique is proposed to calculate regular and singular integrals on quadratic integration cells.
• Three numerical ...

Meshless methods are a type of numerical method used to simulate continuum mechanics problems. These methods have been applied to several types of problems, there are a few works using meshless method focused on dynamic problems, but most works ...

This paper proposes a novel meshless local integral equation (LIE) method for numerical solutions of two and three-dimensional Poisson equations. The proposed method can be regarded as a new variant of the meshless local Petrov-...

Local weak based meshless methods construct weak form of governing equations on local sub-domains. In two dimensional domains, for the simplicity of computations, these sub-domains are taken as circles. In these methods, the optimal radius of sub-...

This paper proposes and analyzes a stabilized element-free Galerkin (EFG) method for meshless Galerkin analysis of the generalized Stokes problem. The Nitsche-type weak form of the generalized Stokes problem is derived by adopting Nitsche's ...

In this study, a meshless approach called Discrete Least Squares Meshless is used to solve the third-order nonlinear Korteweg–de Vries equation numerically. In shallow water, the Korteweg–de Vries equation illustrates the ...

• A truly meshless method is applied for the solution of Korteweg–de Vries equation.

In this paper, a novel meshless method that can handle porous flow problems with singular source terms is developed by virtually constructing node control domains. By defining a connectable node cloud, this method uses the integral of the ...

An element-free Galerkin method (EFGM) is proposed for meshfree numerical analysis of the nonlinear Schrödinger equation. In this method, an explicit linearized scheme with second-order time convergence is proposed to handle the ...

The network element method (NEM), a variational numerical method where the usual mesh was replaced by a discretization network has been recently introduced for the basic Poisson problem. A coercive and stable numerical scheme was ...

• The NEM is extended to heterogeneous and anisotropic diffusion-reaction.
• ...

Projecting reduced-weight components with increased performance is a continuous engineering challenge, especially in the aircraft industry, where fuel consumption, emissions, and performance are highly dependent on structure weight. Nowadays, ...

• A novel meshless approach for phase-field modelling of dendritic growth.
• ...

A novel adaptive numerical approach is developed for an accurate and computationally efficient phase-field modelling of dendritic solidification. The adaptivity is based on the dynamic quadtree domain decomposition. A quadtree ...

Transient nonlinear problems play an important role in many engineering problems. Phase-field equations, including the well-known Allen-Cahn and Cahn-Hilliard equations, fall in this category, and have applications in cutting-edge ...

For very strong convection-dominated problems, stabilized meshless methods such as variational multiscale element-free Galerkin (VMEFG) method may still produce over- and under-shootings near the boundary or interior layers. In this paper, an ...

• A high-accurate meshless method for compressible viscous flows is presented.
• ...

In this work we present a high-accurate discretization to solve the compressible Navier-Stokes equations using an Arbitrary Lagrangian-Eulerian meshless method (SPH-MLS), which can be seen as a general formulation that includes some ...

• Simulation of cell proliferation using a new phenomenological law solved by the Radial Point Interpolation Method (RPIM), a meshless method.

During cell proliferation, cells grow and divide in order to obtain two new genetically identical cells. Understanding this process is crucial to comprehend other biological processes. Computational ...