Infinite element method

Differential equations

Navier–Stokes differential equations used to simulate airflow around an obstruction.

Scope

* Natural sciences
* Engineering

* Astronomy
* Physics
* Chemistry

Biology
* Geology

Applied mathematics

* Continuum mechanics
* Chaos theory
* Dynamical systems

Social sciences

* Economics
* Population dynamics

Classification

Types

* Ordinary
* Partial
* Differential-algebraic
* Integro-differential
* Fractional
* Linear
* Non-linear

By variable type

* Dependent and independent variables

* Autonomous
* Complex
* Coupled / Decoupled
* Exact
* Homogeneous / Nonhomogeneous

Features

* Order
* Operator

* Notation

Relation to processes

* Difference (discrete analogue)

* Stochastic
* Stochastic partial
* Delay

Solution

General topics

* Picard–Lindelöf theorem
* Wronskian

* Phase portrait
* Phase space

* Lyapunov / Asymptotic / Exponential stability
* Rate of convergence
* Series / Integral solutions

* Numerical integration
* Dirac delta function

Solution methods

* Inspection
* Method of characteristics

Euler
* Exponential response formula
* Finite difference (Crank–Nicolson)
* Finite element
* Infinite element
* Finite volume
* Galerkin
* Petrov–Galerkin
* Integrating factor
* Integral transforms
* Perturbation theory
* Runge–Kutta

* Separation of variables
* Undetermined coefficients
* Variation of parameters

People

* Isaac Newton
* Gottfried Leibniz
* Leonhard Euler
* Émile Picard
* Józef Maria Hoene-Wroński
* Ernst Lindelöf
* Rudolf Lipschitz
* Augustin-Louis Cauchy
* John Crank
* Phyllis Nicolson
* Carl David Tolmé Runge
* Martin Kutta

* v
* t
* e

The infinite element method is a numerical method for solving problems of engineering and mathematical physics. It is a modification of finite element method. The method divides the domain concerned into sections of infinite length. In contrast with a finite element which is approximated by polynomial expressions on a finite support, the unbounded length of the infinite element is fitted with functions allowing the evaluation of the field at the asymptote. The number of functions and points of interpolations define the accuracy of the element in the infinite direction.[1] The method is commonly used to solve acoustic problems and allows to respect the Sommerfeld condition of non-return of the acoustic waves and the diffusion of the pressure waves in the far field. [2][3]

## References

1. ↑ Ying, Lung-an (1995). Infinite Element Methods. ISBN 978-3-528-06610-9.
2. ↑ Gerdes, K. (1998). "Infinite Element Methods". IUTAM Symposium on Computational Methods for Unbounded Domains. Fluid Mechanics and its Applications. 49. pp. 143–150. doi:10.1007/978-94-015-9095-2_15. ISBN 978-90-481-5106-6.
3. ↑ Autrique, Jean-Christophe; Magoulès, Frédéric (July 2006). "Studies of an infinite element method for acoustical radiation". Applied Mathematical Modelling 30 (7): 641–655. doi:10.1016/j.apm.2005.08.022. ISSN 0307-904X.

* v
* t
* e

Numerical partial differential equations by method

Finite difference|

| Parabolic|

* Forward-time central-space (FTCS)
* Crank–Nicolson

|

Hyperbolic|

* Lax–Friedrichs
* Lax–Wendroff
* MacCormack
* Upwind
* Method of characteristics

Others|

* Alternating direction-implicit (ADI)
* Finite-difference time-domain (FDTD)

Finite volume|

* Godunov
* High-resolution
* Monotonic upstream-centered (MUSCL)
* Advection upstream-splitting (AUSM)
* Riemann solver
* essentially non-oscillatory (ENO)
* weighted essentially non-oscillatory (WENO)

Finite element|

* hp-FEM
* Extended (XFEM)
* Discontinuous Galerkin (DG)
* Spectral element (SEM)
* Mortar
* Gradient discretisation (GDM)
* Loubignac iteration
* Smoothed (S-FEM)

Meshless/Meshfree|

* Smoothed-particle hydrodynamics (SPH)
* Moving particle semi-implicit method (MPS)
* Material point method (MPM)
* Particle-in-cell (PIC)

Domain decomposition|

* Schur complement
* Fictitious domain
* Schwarz alternating
* additive
* abstract additive
* Neumann–Dirichlet
* Neumann–Neumann
* Poincaré–Steklov operator
* Balancing (BDD)
* Balancing by constraints (BDDC)
* Tearing and interconnect (FETI)
* FETI-DP

Others|

* Spectral
* Pseudospectral (DVR)
* Method of lines
* Multigrid
* Collocation
* Level-set
* Boundary element
* Immersed boundary
* Analytic element
* Particle-in-cell
* Isogeometric analysis
* Infinite difference method
* Infinite element method
* Galerkin method
* Petrov–Galerkin method
* Validated numerics
* Computer-assisted proof

0.00

(0 votes)

Original source: https://en.wikipedia.org/wiki/Infinite element method. Read more

|

Retrieved from "https://handwiki.org/wiki/index.php?title=Infinite_element_method&oldid=181944"
*[v]: View this template
*[t]: Discuss this template
*[e]: Edit this template