The GRACE-based model GGM02S is a global gravity model expressed in spherical harmonics. As the model is a global solution, a certain smoothing of the available gravity field information is unavoidable. For regional geoid determination the irregularities of residual gravity field should be included. The paper presents the global GRACE gravity field solution, regionally improved by adding a residual field, which is represented by radial base functions. The GRACE observations over the territory of Poland are analysed and a regionally improved GRACE geoid from this data is derived. This improved regional geoid is compared with the Polish quasigeoid and differences between the global and regionally improved GRACE GGM02S solutions are discussed. The study shows that the error of the official GRACE GGM02s solution was reduced by 50% due 10 regional refinement.

An efficiency of the nonsingular meshless method (MLM) was analyzed in an acoustic indoor problem. The solution was assumed in the form of the series of radial bases functions (RBFs). Three representative kinds of RBF were chosen: the Hardy’s multiquadratic, inverse multiquadratic, Duchon’s functions. The room acoustic field with uniform, impedance walls was considered. To achieve the goal, relationships among physical parameters of the problem and parameters of the approximate solution were first found. Physical parameters constitute the sound absorption coefficient of the boundary and the frequency of acoustic vibrations. In turn, parameters of the solution are the kind of RBFs, the number of elements in the series of the solution and the number and distribution of influence points. Next, it was shown that the approximate acoustic field can be calculated using MLM with a priori error assumed. All approximate results, averaged over representative rectangular section of the room, were calculated and then compared to the corresponding accurate results. This way, it was proved that the MLM, based on RBFs, is efficient method in description of acoustic boundary problems with impedance boundary conditions and in all acoustic frequencies.