We consider the optimal design of a machine frame under several stress constraints. The shape optimization is based on a Quasi-Newton Method. We need to solve the plain stress state equations in a complex domain for each evaluation of the objective therein. The complexity and robustness of the optimization depends strongly on the solver for the pde. Therefore, solving the direct problem require...

We consider the task of design optimization, where the constraint is a state equation that can only be solved by a typically rather slowly converging fixed point solver. This process can be augmented by a corresponding adjoint solver, and based on the resulting approximate reduced derivatives, also an optimization iteration, which actually changes the design. To coordinate the three iterative p...

A constitutive model based on two–dimensional unstructured Galerkin finite volume method (GFVM) is introduced and applied for analyzing nonlinear behavior of cracked concrete structures in equilibrium condition. The developed iterative solver treats concrete as an orthotropic nonlinear material and considers the softening and hardening behavior of concrete under compression and tension by using...

and Executive Summary In this paper, we test the effect of preprocessed and iterative linear cuts on the convex constraints maximum voltage and maximum current in iterative linear approximation of the current voltage IV formulation of the ACOPF ILIV‐ACOPF problem. The nonconvex constraints are linearized using iterative first order Taylor series approximation. The ILIV‐ACOPF is solved as a sing...

A stochastic version of a stationary linear iterative solver may be designed to converge in distribution to a probability distribution with a specified mean μ and covariance matrix A−1. A common example is Gibbs sampling applied to a multivariate Gaussian distribution which is a stochastic version of the Gauss-Seidel linear solver. The iteration operator that acts on the error in mean and covar...

Some extensions of a modeling system are described that facilitate higher level structure identification within a model. These structures, which often involve complementarity relationships, can be exploited by modern large scale mathematical programming algorithms. A specific implementation of an extended mathematical programming tool is outlined that communicates structure in a computationally...

When powerful machines such as the Cray-2 became available in the late 1980s, a number of researchers investiWe investigate the use of an inexact Newton’s method to solve the potential equations in the transonic regime. As a test case, gated use of exact Newton’s method for solving steady we solve the two-dimensional steady transonic small disturbance state CFD problems. Direct sparse matrix so...

A fast full second order time-step algorithm for some recently proposed nonlinear, nonlocal active models for the inner ear is analyzed here. In particular, we emphasize the properties of discretized systems and the convergence of a hybrid direct-iterative solver for its approximate solution in view of the parameters of the continuous model. We found that the proposed solver is faster than stan...