Accuracy and computing speed of Earth’s Surface Modelling
Keywords
Earth’s surface modelling, fundamental theorem, computing speed, high accuracy, HASM
Start Date
26-6-2018 3:40 PM
End Date
26-6-2018 5:20 PM
Abstract
In terms of the fundamental theorem of Earth’s surface modelling, an Earth’s surface or a component surface of the Earth’s surface environment is uniquely defined by both extrinsic and intrinsic invariants of the surface, which can be simulated with an appropriate method for integrating the extrinsic and intrinsic invariants, such as the method for high accuracy surface modeling (HASM), when the spatial resolution of the surface is fine enough to capture the attribute(s) of interest. HASM was developed initiatively to find solutions for error problem of environmental systems modeling. However, HASM has a huge computation cost because it must use an equation set for simulating each lattice of a surface. To speed up the computation of HASM, we developed a multi-grid method of HASM (HASM-MG), a preconditioned conjugate gradient algorithm of HASM (HASM-PCG), an adaptive method of HASM, and an adjustment computation of HASM (HASMAC). Multi-grid method is the fastest numerical method for solving partial differential equations, which is based on two principles that are error smoothing and coarse grid correction. The preconditioned conjugate gradient algorithm can be developed by introducing a preconditioner to ensure faster convergence of the conjugate gradient method. The principle of the adaptive method is that grid cells where the error is large will be marked for refinement, while grid cells with a satisfied accuracy are left unchanged. The adjustment computation permits all observations to be entered into the adjustment and used simultaneously in the computations by means of least squares.
Accuracy and computing speed of Earth’s Surface Modelling
In terms of the fundamental theorem of Earth’s surface modelling, an Earth’s surface or a component surface of the Earth’s surface environment is uniquely defined by both extrinsic and intrinsic invariants of the surface, which can be simulated with an appropriate method for integrating the extrinsic and intrinsic invariants, such as the method for high accuracy surface modeling (HASM), when the spatial resolution of the surface is fine enough to capture the attribute(s) of interest. HASM was developed initiatively to find solutions for error problem of environmental systems modeling. However, HASM has a huge computation cost because it must use an equation set for simulating each lattice of a surface. To speed up the computation of HASM, we developed a multi-grid method of HASM (HASM-MG), a preconditioned conjugate gradient algorithm of HASM (HASM-PCG), an adaptive method of HASM, and an adjustment computation of HASM (HASMAC). Multi-grid method is the fastest numerical method for solving partial differential equations, which is based on two principles that are error smoothing and coarse grid correction. The preconditioned conjugate gradient algorithm can be developed by introducing a preconditioner to ensure faster convergence of the conjugate gradient method. The principle of the adaptive method is that grid cells where the error is large will be marked for refinement, while grid cells with a satisfied accuracy are left unchanged. The adjustment computation permits all observations to be entered into the adjustment and used simultaneously in the computations by means of least squares.
Stream and Session
A3: Simulation, Optimization, and Metamodelling: Tradeoffs of Speed, Resource Utilization, and Accuracy