**Multi-material Structural Topology Optimization:**

A computationally efficient framework for multi-material continuum based structural topology optimization is available in Plato. This state-of-the-art framework leads to a setting in which sufficiently general volume/mass constraints can be specified. For instance,

- Each volume/mass constraint can control all or a subset of the candidate materials
- The volume/mass constraint can control the entire domain or a sub-region of the domain
- A subset of the candidate materials can be specified for the entire domain or each sub-region of the domain
- There is no limit to the number of candidate materials in a subset

**Uncertainty Aware Structural Topology Optimization:**

This work presents a structural topology optimization strategy for the quantification and propagation of uncertainties via stochastic reduced order modeling techniques. Uncertainty aware optimization problems can be computationally complex due to the multiple model evaluations that are necessary to accurately quantify and propagate uncertainties. This computational complexity can be greatly magnified if a high fidelity, physics-based model is used for the structural topology optimization calculations. Plato is developing a generic, computationally efficient approach to effectively 1) alleviate the prohibitive computational cost associated with an uncertainty aware structural topology optimization problem; and 2) quantify and propagate the inherent uncertainties due to design imperfections.

**Level-Set Methods for Synthesis Optimization:**

Plato is investigating level-set specifically for large-scale optimization. Level-set methods allow the definition of crisp interfaces between distinct material phases implicitly by iso-contours of a level-set function. A core advantage of level set methods is that it allows a crisp description of the boundaries. This improves the accuracy with which the physics response is captured during optimization. The choice of the level set function parameterization also determines the kind of design freedom available during synthesis optimization. This flexibility enables the user to explore multiple synthesis optimization options (shape, topology, both) when designing a part.

**Massively Parallel Kernel Filter:**

Plato uses a kernel filter built specifically for rapid construction and usage on many parallel processors. Kernel filters are used in structural topology optimization as a projection step from abstract design variables to physical design variables; this projection step allows for smooth design surfaces and indirectly defines an approximate minimum length scale for structural members. The kernel filter is a large, sparse, and parallel matrix stored in non-redundant sections on each processor in the compressed sparse row format. The kernel filter matrix is a square matrix of size number of mesh nodes by number of mesh nodes; the entries of the kernel filter matrix are zero except for entries where that row's node and that column's node are within a filter radius. Finding mesh nodes within the filter radius is the fixed radius nearest neighbor's problem, and can be solved rapidly for millions of nodes by spatial searching techniques.