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We then formulate adaptive mesh-refining algorithms for each of these three approaches.
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In particular, our analysis gives a first contribution to adaptive BEM in the frame of isogeometric analysis (IGABEM), for which we formulate an adaptive algorithm which steers the local mesh-refinement and the multiplicity of the knots.
Based on knot insertion, we formulate an adaptive algorithm which is capable to control and adapt the multiplicity of the nodes as well as the local mesh-size (Algorithm 4.5).
We formulate an adaptive Riemannian metric consistent with this theorem.
Then, the covariance-fitting-based algorithm and the Kalman filtering theory are combined to formulate an adaptive tracking algorithm.
We formulate the adaptive beamspace design problem as a second-order cone program (SOCP) that can be solved efficiently using interior point methods.
In the controller design, the approximation capabilities of fuzzy systems are employed to identify the unknown functions, formulate suitable adaptive control law and updating algorithms for the controller parameters.
□ Before we formulate an adaptive algorithm based on NURBS, we recall refinement by knot-insertion, see e.g. [23, Section 11].
This additional information is used to formulate a fully adaptive algorithm including adaptive stopping criteria for iterative solvers as well as refinement/derefinement criteria for both the time step and the mesh size.
Based on this error estimator, we formulated an adaptive algorithm for IGABEM, which uses h -refinement as well as multiplicity increase of the knots for refinement.
The SOoA is pivotal in a refined version of a recently-introduced methodology for formulating excitation-adaptive wave equation FDTD (WE-FDTD) schemes, described below.
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