No abstract

In calculating expected information gain in optimal Bayesian experimental design, the computation of the inner loop in the classical double-loop Monte Carlo requires a large number of samples and suffers from underflow if the number of samples is small. These drawbacks can be avoided by using an importance sampling approach. We present a computationally efficient method for optimal Bayesian experimental design that introduces importance sampling based on the Laplace method to the inner loop. We derive the optimal values for the method parameters in which the average computational cost is minimized according to the desired error tolerance. We use three numerical examples to demonstrate the computational efficiency of our method compared with the classical double-loop Monte Carlo, and a more recent single-loop Monte Carlo method that uses the Laplace method as an approximation of the return value of the inner loop. The first example is a scalar problem that is linear in the uncertain parameter. The second example is a nonlinear scalar problem. The third example deals with the optimal sensor placement for an electrical impedance tomography experiment to recover the fiber orientation in laminate composites.

SUMMARYWe introduce several extensions to subdivision shells that provide an improved level of shape control over shell boundaries and facilitate the analysis of shells with non-smooth and non-manifold joints. To this end, extended subdivision schemes are used that enable to relax the continuity of the limit surface along prescribed crease edges and to create surfaces with prescribed limit positions and normals. Furthermore, shells with boundaries in the form of conic sections, such as circles or parabolas, are represented with rational subdivision schemes, which are defined in analogy to rational b-splines. In terms of implementation, the difference between the introduced and conventional subdivision schemes is restricted to the use of modified subdivision stencils close to the mentioned geometric features. Hence, the resulting subdivision surface is in most parts of the domain identical to standard smooth subdivision surfaces. The particular subdivision scheme used in this paper constitutes an extended version of the original Loop's scheme and is as such based on triangular meshes. As in the original subdivision shells, surfaces created with the extended subdivision schemes are used for interpolating the reference and deformed shell configurations. At the integration points, the subdivision surface is evaluated using a newly developed discrete parameterization approach. In the resulting finite elements, the only degrees of freedom are the mid-surface displacements of the nodes and additional Lagrange parameters for enforcing normal constraints. The versatility of the newly developed elements is demonstrated with a number of geometrically nonlinear shell examples.

No abstract