In this paper, the authors consider a parametrized non-linear parabolic differential equation, which is motivated by lithium-ion battery models. A standard finite volume discretization leads to a high-dimensional discrete non-linear problem so that simulation of the parametrized problem for various different parameters is very costly. Therefore, the reduced-basis method is applied, so that the number of degrees of freedom is reduced significantly and a fast numerical simulation of the model is possible. To control the error, an a-posteriori error estimator is derived. Numerical experiments show the efficiency of the approach.@en

The aim of this work is to solve parametrized partial differential equations in computational domains represented by networks of repetitive geometries by combining reduced basis and domain decomposition techniques. The main idea behind this approach is to compute once, locally and for few reference shapes, some representative finite element solutions for different values of the parameters and with a set of different suitable boundary conditions on the boundaries: these functions will represent the basis of a reduced space where the global solution is sought for. The continuity of the latter is assured by a classical domain decomposition approach. Test results on Poisson problem show the flexibility of the proposed method in which accuracy and computational time may be tuned by varying the number of reduced basis functions employed, or the set of boundary conditions used for defining locally the basis functions. The proposed approach simplifies the pre-computation of the reduced basis space by splitting the global problem into smaller local subproblems. Thanks to this feature, it allows dealing with arbitrarily complex network and features more flexibility than a classical global reduced basis approximation where the topology of the geometry is fixed.@en

In this paper the reduced basis (RB) method is applied to solve quadratic multiobjective optimal control problems governed by linear parametrized variational equations. These problems often arise in applications, where the quality of the system behavior has to be measured by more than one criterium. The weighted sum method is exploited for defining scalar-valued linear-quadratic optimal control problems built by introducing additional optimization parameters. The optimal controls corresponding to specific choices of the optimization parameters are efficiently computed by the RB method. The accuracy is guaranteed by an a-posteriori error estimate. An effective sensitivity analysis allows to further reduce the computational times for identifying a suitable and representative set of optimal controls.@en

Residual stresses are common in Micro Electro Mechanical System (MEMS) membrane structures. Experimental assessment of these stresses can provide valuable information on the production process. In general, experimental stress assessment for MEMS is challenging due to the limited possibilities for non-destructive testing. This work investigates the use of dynamic modal data to identify the residual stress state. In view of the computational feasibility, the focus is on two aspects: 1) A method is proposed that expresses the unknown stress field as a combination of few, carefully selected stress modes. An optimization algorithm is deemed to identify the amplitudes of such modes. 2) A meta-model is constructed using the empirical interpolation method (EIM), to facilitate a fast evaluation of the iterations.@en

In this paper a reduced-order strategy is applied to solve a multiobjective optimal control problem governed by semilinear parabolic partial differential equations. These problems often arise in practical applications, where the quality of the system behaviour has to be measured by more than one criterium. The weighted sum method is exploited for defining scalar-valued nonlinear optimal control problems built by introducing additional optimization parameters. The optimal controls corresponding to specific choices of the optimization parameters are efficiently computed by the reduced-basis method. The accuracy is guaranteed by an a-posteriori error estimate.@en