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Abaqus FEA [4] [5] (formerly ABAQUS) is a software suite for finite element analysis and computer-aided engineering, originally released in 1978. The name and logo of this software are based on the abacus calculation tool. [6] The Abaqus product suite consists of five core software products: [5]
The Newmark-beta method is a method of numerical integration used to solve certain differential equations.It is widely used in numerical evaluation of the dynamic response of structures and solids such as in finite element analysis to model dynamic systems.
Nodal integration has been proposed as a technique to use finite elements to emulate a meshfree behaviour. [citation needed] However, the obstacle that must be overcome in using nodally integrated elements is that the quantities at nodal points are not continuous, and the nodes are shared among multiple elements.
The boundary element method (BEM) is a numerical computational method of solving linear partial differential equations which have been formulated as integral equations (i.e. in boundary integral form), including fluid mechanics, acoustics, electromagnetics (where the technique is known as method of moments or abbreviated as MoM), [1] fracture mechanics, [2] and contact mechanics.
Leapfrog integration is equivalent to updating positions () and velocities () = ˙ at different interleaved time points, staggered in such a way that they "leapfrog" over each other. Leapfrog integration is a second-order method, in contrast to Euler integration , which is only first-order, yet requires the same number of function evaluations ...
What follows is the Richtmyer two-step Lax–Wendroff method. The first step in the Richtmyer two-step Lax–Wendroff method calculates values for f(u(x, t)) at half time steps, t n + 1/2 and half grid points, x i + 1/2. In the second step values at t n + 1 are calculated using the data for t n and t n + 1/2.
The number and location of the grid points together with a corresponding set of integration weights are determined by enforcing the exact integration of polynomials (or equivalently, spherical harmonics) up to a given order, leading to a sequence of increasingly dense grids analogous to the one-dimensional Gauss-Legendre scheme.
Gauss–Kronrod formulas are extensions of the Gauss quadrature formulas generated by adding + points to an -point rule in such a way that the resulting rule is exact for polynomials of degree less than or equal to + (Laurie (1997, p. 1133); the corresponding Gauss rule is of order ).
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