Optimal-Transportation Meshfree Approximation Schemes - Solid ...
Optimal-Transportation Meshfree Approximation Schemes - Solid ...
Optimal-Transportation Meshfree Approximation Schemes - Solid ...
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<strong>Optimal</strong>-<strong>Transportation</strong> <strong>Meshfree</strong> (OTM)<br />
• <strong>Optimal</strong> transportation theory is a useful<br />
tool for generating geometrically-exact<br />
geometrically exact<br />
discrete Lagrangians for flow problems<br />
• Inertial part of discrete Lagrangian<br />
measures distance between consecutive<br />
mass densities (in sense of Wasserstein)<br />
• Di Discrete t HHamilton ilt principle i i l of f stationary t ti<br />
action: Variational time integration scheme:<br />
– Symplectic Symplectic, time reversible<br />
– Exact conservation properties (linear and angular<br />
momenta, energy)<br />
– S Strong variational i i l convergence i in the h sense of f Γ-<br />
convergence (B. Schmidt)<br />
Michael Ortiz<br />
UCLA 02/22/10
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