Contents
1. Introduction	1
2. Simulation Methods	5
2.1. Quantum Mechanics	5
2.2. Atomistic Techniques	6
2.2.1. Monte Carlo	7
2.2.2. Molecular Dynamics	8
2.3. Mesoscale Techniques	9
2.3.1. Brownian Dynamics	10
2.3.2. Dissipative Particle Dynamics	11
2.3.3. Lattice Boltzmann	12
2.4. Macroscale Techniques	14
2.4.1. Finite Element Method	15
2.4.2. Finite Volume Method	17
3. Multiscale Strategies	19
3.1. Sequential Multiscale Approaches	19
3.1.1. Systematic Coarse-Graining Methods	22
3.1.1.1. Low Coarse-Graining Degrees	23
3.1.1.2. Medium Coarse-Graining Degrees	26
3.1.1.3. High Coarse-Graining Degrees	29
3.1.2. Reverse Mapping	30
3.2. Concurrent Multiscale Approaches	33
3.2.1. The Concept of Handshaking	34
3.2.2. Linking Atomistic and Continuum Models	35
3.2.2.1. Quasicontinuum Approach	37
3.2.2.2. Coarse-Grained Molecular Dynamics	39
3.2.2.3. Finite-element/Atomistic Method	39
3.2.2.4. Bridging Scale Method	40
3.2.2.5. Applications in Polymeric Materials	41
3.3. Adaptive Resolution Simulations	42
3.3.1. The Adaptive Resolution Scheme	43
3.3.2. The Hamiltonian Adaptive Resolution Scheme	45
3.4. Extending Atomistic Simulations	47
4. Conclusions and Outlooks	49
Appendix A. Acronyms and Nomenclature	51
References	56