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The high-order methods is difficultly applied in various elements. The development of a 3D solver by using the spectral difference method of unstructured grids via mixed elements is presented. A mixed tri-prism and tetrahedral grid is firstly refined using one-level h-refinement to generate a hexahedral grid while keeping the curvature of wall boundaries. The SD method designed for hexahedral elements can subsequently be applied for refining the unstructured grid. Through a series of numerical tests, the present method is high-order accurate for both inviscid and viscous flows is demonstrated; the results obtained for inviscid and viscous compressible flows compare well with other published results.

For the parallel solution of structural finite element problem with non-matching multi-domains, a nonmatched finite element tearing and interconnectiong (FETI) parallel algorithm is proposed based on L-FETI method by introducing the frame node force and modifying the frame displacement compatibility condition and the load balance condition. Based on the radial basis functions (RBF) interpolation technique, the data transfer of internal force and displacement between the neighboring subdomains has a unified matrix format and is easy to program by introducing a local coordinate system into the non-matching interfaces. Taking the finite element model for plate bending problem with four subdomains as an example, two kinds of multi-domains models, matching and non-matching meshes, are constructed respectively. The numerical results show that the out-of-plane deflection of the same nodes on the domain decomposition frame is in a good agreement, which shows that the present method is reasonable and effective for solving the parallel non-matching multi-domains model.