Difference between revisions of "MPM Methods and Simulation Timing"
(Created page with "below. These command set up the MPM method used and timing information: * MPMMethod Command * PtsPerElement Command * TimeStep Command * MaximumTime Command *...") |
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These command select the MPM method to use and control time step and total time for the simulation. | |||
== Theory == | |||
Many tasks in MPM involve extrapolations from particles to the grid or from the grid to the particles. These extrapolations are controlled by "Shape Functions," and the various MPM methods correspond to various methods for evaluating the shape functions. In the most generalized description of MPM (called GIMP for Geneal Interpolation Material Point), the shape function and shape function gradient for the node i/particle p pair are: | |||
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<math>S_{ip} = {\int_{\Omega_p} \chi_p(\vec x)N_i(\vec x) dV\over \int_{\Omega_p} \chi_p(\vec x) dV}\qquad{\rm and}\qquad G_{ip} = {\int_{\Omega_p} \chi_p(\vec x)\nabla N_i(\vec x) dV\over \int_{\Omega_p} \chi_p(\vec x) dV}</math> | |||
* [[MPMMethod Command]] | * [[MPMMethod Command]] | ||
Revision as of 16:21, 5 September 2013
These command select the MPM method to use and control time step and total time for the simulation.
Theory
Many tasks in MPM involve extrapolations from particles to the grid or from the grid to the particles. These extrapolations are controlled by "Shape Functions," and the various MPM methods correspond to various methods for evaluating the shape functions. In the most generalized description of MPM (called GIMP for Geneal Interpolation Material Point), the shape function and shape function gradient for the node i/particle p pair are:
[math]\displaystyle{ S_{ip} = {\int_{\Omega_p} \chi_p(\vec x)N_i(\vec x) dV\over \int_{\Omega_p} \chi_p(\vec x) dV}\qquad{\rm and}\qquad G_{ip} = {\int_{\Omega_p} \chi_p(\vec x)\nabla N_i(\vec x) dV\over \int_{\Omega_p} \chi_p(\vec x) dV} }[/math]