A noise-vibration-harshness (NVH) design optimization of a complex vehicle structure is presented using finite element and boundary element analyses. The steady-state dynamic behavior of the vehicle is calculated from the frequency response finite element analysis, while the sound pressure level within the acoustic cavity is calculated from the boundary element analysis. A reverse solution proc...

We present a new continuous adjoint method for Aerodynamic Shape Optimization (ASO) using the Euler equations, which reduces the computational cost of the gradients by reducing the volume integral part of the adjoint gradient formula to a surface integral. The savings are particularly significant for three-dimensional ASO problems on general unstructured and overset meshes. In order to validate...

This paper describes an algorithm for PDE-constrained optimization that controls numerical errors using error estimates and grid adaptation. A key aspect of the algorithm is the use of adjoint variables to estimate errors in the first-order optimality conditions. Multilevel optimization is used to drive the optimality conditions and their estimated errors below a specified tolerance. The error ...

This paper deals with a control-constrained linear-quadratic optimal control problem governed by the Stokes equations. It is concerned with situations where the gradient of the velocity field is not bounded. The control is discretized by piecewise constant functions. The state and the adjoint state are discretized by finite element schemes that are not necessarily conforming. The approximate co...

On the half line 0; 1) we study rst order diierential operators of the form B 1 i d dx + Q(x); where B := B 1 0 0 ?B 2 ; B 1 ; B 2 2 M(n; C) are self{adjoint positive deenite matrices and Q : R + ! M(2n; C); R + := 0; 1); is a continuous self{adjoint oo{diagonal matrix function. We determine the self{adjoint boundary conditions for these operators. We prove that for each such boundary value pro...

In this paper, a problem of shape design for a duct with the flow governed by the one-dimensional Euler equations is analyzed. The flow is assumed to be transonic, in the sense that we have a shock embedded in the flow. The presence of the shock introduces analytical and numerical difficulties that are overcome by introducing the shock location as an explicit state variable. We justify the use ...

We investigate the reasons for which the existence of certain right adjoints implies the existence of some final coalgebras, and vice-versa. In particular we prove and discuss the following theorem which has been partially available in the literature: let F a G be a pair of adjoint functors, and suppose that an initial algebra F̂ (X) of the functor H(Y ) = X + F (Y ) exists; then a right adjoint...

We study practical strategies for estimating numerical errors in scalar outputs calculated from unsteady simulations of convection-dominated flows, including those governed by the compressible Navier–Stokes equations. The discretization is a discontinuous Galerkin finite element method in space and time on static spatial meshes. Time-integral quantities are considered for scalar outputs and the...