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Optimization Methods on Riemannian Manifolds and Their Application to Shape Space
We extend the scope of analysis for linesearch optimization algorithms on (possibly infinite-dimensional) Riemannian manifolds to the convergence analysis of the BFGS quasi-Newton scheme and the
Effect of non-linear permeability in a spherically symmetric model of hydrocephalus.
A spherically symmetric model of the brain is examined and non-linear effects tend to improve predictions of ventricle wall displacement and pressure increase in acute hydrocephalus in comparison with a constant permeability model.
An axisymmetric and fully 3D poroelastic model for the evolution of hydrocephalus.
The equations for axisymmetric and fully 3D models of a hydrocephalic brain are formulated and the effect of hydrostatic pressure variation is considered.
Time‐Discrete Geodesics in the Space of Shells
A computational model for geodesics in the space of thin shells, with a metric that reflects viscous dissipation required to physically deform a thin shell, is offered, which emphasizes the strong impact of physical parameters on the evolution of a shell shape along a geodesic path.
A Nonlinear Elastic Shape Averaging Approach
A physically motivated approach is presented for computing a shape average of a given number of shapes, which minimizes the total elastic energy stored in these deformations and is invariant under rigid body motions.
A Continuum Mechanical Approach to Geodesics in Shape Space
The proposed shape metric is derived from a continuum mechanical notion of viscous dissipation and implemented via a level set representation of shapes, and a finite element approximation is employed as spatial discretization both for the pairwise matching deformations and for the level set representations.
Variational time discretization of geodesic calculus
We analyze a variational time discretization of geodesic calculus on finite- and certain classes of infinite-dimensional Riemannian manifolds. We investigate the fundamental properties of discrete
Differentiable Piecewise-Bézier Surfaces on Riemannian Manifolds
This work generalizes the notion of Bezier surfaces and surface splines to Riemannian manifolds and proposes an algorithm to optimize the BeZier control points given a set of points to be interpolated by a Beziers surface spline.
Analytic solution during an infusion test of the linear unsteady poroelastic equations in a spherically symmetric model of the brain.
This work determines the spatial and temporal distribution of cerebrospinal fluid (CSF) pressure and brain displacement during an infusion test in a spherically symmetric, three-component poroelastic model of the brain.
A simple and efficient scheme for phase field crystal simulation
We propose an unconditionally stable semi-implicit time discretization of the phase field crystal evolution. It is based on splitting the underlying energy into convex and concave parts and then