I. First steps towards modeling a multi-scale earth system, 1. Introduction, 2. Multiscale Non-Equilibrium Thermodynamics, 3. Mathematical Formulation II. 3D Mesh Generation in Geocomputing, 1. Introduction, 2. Goemetrical Modeling, 3. Hexahedral Mesh Generation, 4. Tetrahedral Mesh Generation, 5. Conclusions III. Strategies for Preconditioning Methods of Parellel Iterative Solver for Finite-Element Applications in Geophysics, 1. Background, 2. Various Approaches for Parallel Preconditioning Methods in III-Conditioned Probelms, 3. Examples: Contact Problems, 4. Examples: Linear Elastic Problems with Heterogeneous Material Properties, 5. Concluding Remarks, 6. Appendix 1 Parallel Iterative Solvers in GeoFEM IV. Algorithms for Optimizing Rheology and Loading Forces in Finite Element Models for Lithospheric Deformation, 1. Introduction, 2. Methodology, 3. A Plate Flexural Model, 4. A Three-Dimensional Viscous Model of Lithospheric Deformation, 5. Discussions and Conclusions V. Mantle Dynamics - A Case Study, 1. Introduction, 2. Physics of Mantle Convection: Basic Equations, 3. Case Study in Global Models of the Earth's Mantle VI. The ESyS_Particle: A New 3-D Discrete Element Model with Single Particle Rotation, 1. Introduction: A Review of the Discrete Element Method, 2. The Model, Equations and Numerical Algorithms, 3. Contct Laws, Particle Interactions and Calculation of Forces and Torques, 4. Parameter Calibration, 5. Some Recent Simulation Results, 6. Disscussion: Major Differences of the ESyS_Particle, 7. Conclusions VII. The Terashake Computational Platform for Large-Scale Earthquake Simulations, 1. Introduction, 2. The TeraShake Computational Platform, 3. The Terashake Application: Anelastic Wave Model, 4. Enhancement and Optimization of the Terashake Application, 5. Data Archival and Management, 6. TeraShake Visualization, 7. Scientific Results of Tera-Shake-1 and TeraShake 2, 8. Lessons Learned from Enabling Very-Large Scale Earthquake SImulations, 9. Summary VIII. Probabilistic Forecast of Tsunami Hazards along Chinese Coast, 1. Introduction, 2. Geological and Geophysical Analysis, 3. Probabilistic Forecast of Tsunami Hazards, 4. Probabilistic Forecst of Tsunami and Seismic Hazard in Eastern China Sea Region, 5. Discussions and Summary, 6. Conclusion