Weakly normal basis vector fields in RKHS with an application to shape Newton methods
A Paganini, K Sturm - SIAM Journal on Numerical Analysis, 2019 - SIAM
SIAM Journal on Numerical Analysis, 2019•SIAM
We construct a space of vector fields that are normal to differentiable curves in the plane. Its
basis functions are defined via saddle point variational problems in reproducing kernel
Hilbert spaces (RKHSs). First, we study the properties of these basis vector fields and show
how to approximate them. Then, we employ this basis to discretize shape Newton methods
and investigate the impact of this discretization on convergence rates.
basis functions are defined via saddle point variational problems in reproducing kernel
Hilbert spaces (RKHSs). First, we study the properties of these basis vector fields and show
how to approximate them. Then, we employ this basis to discretize shape Newton methods
and investigate the impact of this discretization on convergence rates.
We construct a space of vector fields that are normal to differentiable curves in the plane. Its basis functions are defined via saddle point variational problems in reproducing kernel Hilbert spaces (RKHSs). First, we study the properties of these basis vector fields and show how to approximate them. Then, we employ this basis to discretize shape Newton methods and investigate the impact of this discretization on convergence rates.
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