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Finite point method information


The finite point method (FPM) is a meshfree method for solving partial differential equations (PDEs) on scattered distributions of points. The FPM was proposed in the mid-nineties in (Oñate, Idelsohn, Zienkiewicz & Taylor, 1996a),[1] (Oñate, Idelsohn, Zienkiewicz, Taylor & Sacco, 1996b)[2] and (Oñate & Idelsohn, 1998a)[3] with the purpose to facilitate the solution of problems involving complex geometries, free surfaces, moving boundaries and adaptive refinement. Since then, the FPM has evolved considerably, showing satisfactory accuracy and capabilities to deal with different fluid and solid mechanics problems.

  1. ^ Cite error: The named reference Onate1996a was invoked but never defined (see the help page).
  2. ^ Cite error: The named reference Onate1996b was invoked but never defined (see the help page).
  3. ^ Cite error: The named reference Onate1998a was invoked but never defined (see the help page).

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Finite point method

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The finite point method (FPM) is a meshfree method for solving partial differential equations (PDEs) on scattered distributions of points. The FPM was...

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analysis, finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences...

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a topic in mathematics, the spectral element method (SEM) is a formulation of the finite element method (FEM) that uses high-degree piecewise polynomials...

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Finite difference

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quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential...

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Meshfree methods

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the velocity field. Numerical methods such as the finite difference method, finite-volume method, and finite element method were originally defined on meshes...

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Numerical methods for partial differential equations

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volume" refers to the small volume surrounding each node point on a mesh. In the finite volume method, volume integrals in a partial differential equation...

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Smoothed finite element method

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Smoothed finite element methods (S-FEM) are a particular class of numerical simulation algorithms for the simulation of physical phenomena. It was developed...

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Secant method

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can be thought of as a finite-difference approximation of Newton's method. However, the secant method predates Newton's method by over 3000 years. For...

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FPM

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In applied mathematics, the name finite pointset method is a general approach for the numerical solution of problems in continuum mechanics, such as the...

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Partial differential equation

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volume" refers to the small volume surrounding each node point on a mesh. In the finite volume method, surface integrals in a partial differential equation...

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other mesh-based methods like the finite element method, finite volume method or finite difference method, the MPM is not a mesh based method and is instead...

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This is a list of notable software packages that implement the finite element method for solving partial differential equations. This table is contributed...

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point for more rapidly converging methods. The method is also called the interval halving method, the binary search method, or the dichotomy method....

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Finite impulse response

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processing, a finite impulse response (FIR) filter is a filter whose impulse response (or response to any finite length input) is of finite duration, because...

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Euler method in calculating the re-entry of astronaut John Glenn from Earth orbit. Crank–Nicolson method Gradient descent similarly uses finite steps...

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method Finite element method Finite volume method for unsteady flow Fluid animation Immersed boundary method Lattice Boltzmann methods List of finite...

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Finite difference coefficient

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needed]. Finite difference method Finite difference Five-point stencil Numerical differentiation Fornberg, Bengt (1988), "Generation of Finite Difference...

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Closest point method

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method uses standard numerical approaches such as finite differences, finite element or spectral methods in order to solve the embedding partial differential...

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modeled by finite element methods); matrix products (when using transfer matrix methods); calculating numerical integrals (when using the method of moments);...

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these methods would not reach the solution within a finite number of steps (in general). Examples include Newton's method, the bisection method, and Jacobi...

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from method to method. Finite differences are usually the cheapest on a per grid point basis followed by the finite element method and spectral method. However...

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