Using path integral method (Fujikawa’s method) we calculate anomalies in noncommutative gauge theories with fermions in the bi-fundamental and adjoint representation. We find that axial and chiral gauge anomalies coming from non-planar contributions are derived in the low noncommutative momentum limit p̃μ(≡ θpν) → 0. The adjoint chiral fermion carries no anomaly in non-planar sector in D = 4k(k ...

— Two essentially dual, finite element methods for approximating the solution of the boundary value p rob le m Lu =• V ( Ö V « ) + b • V u + cu — f on Q, a rectangle•, with u = O on dCl are shown to give optimal order convergence. The local H~ method is based on the inner product («, L* v) and the adjoint method on {Lu, v). Discontinuons spaces can be employed for the approximate solution in th...

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...

A continuous adjoint approach to aerodynamic design for viscous compressible flows on unstructured grids is developed, and three important problems raised in the continuous adjoint literature are solved: using tools of shape deformation of boundary integrals a generic adjoint formulation is developed with independence of the kind of mesh used; a systematic way of reducing the 2 order derivative...

A novel approach for designing an error measure to guide an adaptive meshing algorithm using a POD adjoint or goal-based method, is presented here. In this work the multi-field error measure was applied to each field type at each time level between two points in time where mesh adaptivity is applied. The aim is to obtain a new mesh that can resolve all the fields at all time levels, to an optim...

In this paper, the exact discrete adjoint of an unstructured finite-volume formulation of the Euler equations in two dimensions is derived and implemented. The adjoint equations are solved with the same implicit scheme as used for the flow equations. The scheme is modified to efficiently account for multiple functionals simultaneously. An optimization framework, which couples an analytical shap...

The paper investigates boundary optimal controls and parameter estimates to the well-posedness nonlinear model of dehydratation of thermic problems. We summarize the general formulations for the boundary control for initial-boundary value problem for nonlinear partial differential equations modeling the heat transfer and derive necessary optimality conditions, including the adjoint equation, fo...