A Multi-Grid Method of High Accuracy Surface Modeling and Its Validation

A method of high accuracy surface modeling (HASM) has been constructed to find a solution for error problems that had long troubled surface modeling in geographical information systems (GIS). It is found that when a preconditioned conjugate gradient (PCG) algorithm is used to solve the large sparse linear system, which HASM can be transferred into, HASM performs best in terms of simulation compared with all other algorithms. But its computing speed is not fast enough for all applications. A multi-grid method is introduced into HASM to try to shorten its computing time. Both numerical and real-world tests demonstrate that there is a range of stop error (SE). The multi-grid method of HASM (HASM-MG) greatly increases computing speed when SEs are within this range, compared with the PCG algorithm of HASM (HASM-PCG). HASM-MG is suitable for applications with a need for less accuracy and a shorter computing time. HASM-PCG is appropriate for issues needing higher accuracy. HASM-MG performs better than HASM-PCG in flat areas, while HASM-PCG does better in complex terrainm in terms of accuracy and computing time.