Simulating heat flux in additive manufacturing

1. A method comprising:

converting a model of an object into a three-dimensional node representation of the object, wherein the node representation includes one or more layers of nodes, and wherein each layer of the one or more layers of nodes corresponds to a layer of material to be added in an additive manufacturing process;

generating, using distances between nodes of the node representation, an adjacency matrix of the object, wherein the adjacency matrix represents each of the one or more layers of nodes in the node representation;

simulating an additive manufacturing process of the object, the simulating comprising, for each layer of the one or more layers of nodes represented in the adjacency matrix:

applying a simulated heat to the layer of the adjacency matrix, and

estimating, using the adjacency matrix, a diffusion of heat to other nodes based on the applied simulated heat; and

generating a representation of an estimated heat distribution within the object.

2. The method of claim 1 , wherein generating the adjacency matrix of the object comprises:

defining layers of nodes by sorting nodes of the node representation based on respective z-coordinates of the nodes;

defining hatches of nodes by sorting the nodes of the node representation based on respective y-coordinates of the nodes; and

building the adjacency matrix based on relationships between the nodes.

3. The method of claim 1 , wherein the representation of the estimated heat distribution within the object comprises a representation of heat flux within the object.

4. The method of claim 1 , wherein the representation of the estimated heat distribution within the object comprises a representation of temperature distribution within the object.

5. The method of claim 1 , further comprising approximating the heat in the object as a function of eigenvectors (ϕ) and eigenvalues (Λ) of a Laplacian matrix derived from the adjacency matrix.

6. The method of claim 1 , further comprising applying data representing the estimated heat distribution within the object as an input to a finite element analysis to obtain an estimate of physical distortions to the object caused by the heat distribution.

7. The method of claim 1 , wherein converting the model of the object into the node representation of the object comprises generating the nodes of the node representation by randomly sampling spatial locations within the model.

8. The method of claim 1 , wherein generating the adjacency matrix of the object comprises, for each node, determining pairwise distances between the node and neighboring nodes that within a neighbor distance, ε, of the node.

9. The method of claim 1 , wherein generating the adjacency matrix of the object comprises determining a matrix weight, a ij , for each pair of nodes that are within a neighbor distance, ε, of each other.

10. The method of claim 9 , wherein each matrix weight, a ij , is determined from:

a

i

⁢

j

=

{

e

-

(

π

i

-

π

j

)

2

σ

2

,

(

π

i

-

π

j

)

2

≤

ϵ

0

,

(

π

i

-

π

j

)

2

>

ϵ

,

where

⁢

(

π

i

-

π

j

)

2

is the square of the distance between nodes π i and π j and σ is the standard deviation of pairwise distances between nodes.

11. An additive manufacturing heat transfer simulation system comprising:

at least one processor; and a data store coupled to the at least one processor having instructions stored thereon which, when executed by the at least one processor, causes the at least one processor to perform operations comprising:

converting a model of an object into a three-dimensional node representation of the object, wherein the node representation includes one or more layers of nodes, and wherein each layer of the one or more layers of nodes corresponds to a layer of material to be added in an additive manufacturing process;

generating, using distances between nodes of the node representation, an adjacency matrix of the object, wherein the adjacency matrix represents each of the one or more layers of nodes in the node representation;

simulating an additive manufacturing process of the object, the simulating comprising, for each layer of the one or more layers of nodes represented in the adjacency matrix:

applying a simulated heat to the layer of the adjacency matrix, and

estimating, using the adjacency matrix, a diffusion of heat to other nodes based on the applied simulated heat; and

generating a representation of an estimated heat distribution within the object.

12. The system of claim 11 , wherein generating the adjacency matrix of the object comprises:

defining layers of nodes by sorting nodes of the node representation based on respective z-coordinates of the nodes;

defining hatches of nodes by sorting the nodes of the node representation based on respective y-coordinates of the nodes; and

building the adjacency matrix based on relationships between the nodes.

13. The system of claim 11 , wherein the representation of the estimated heat distribution within the object comprises a representation of heat flux within the object.

14. The system of claim 11 , wherein the representation of the estimated heat distribution within the object comprises a representation of temperature distribution within the object.

15. The system of claim 11 , wherein the operations further comprise approximating the heat in the object as a function of eigenvectors (ϕ) and eigenvalues (Λ) of a Laplacian matrix derived from the adjacency matrix.

16. The system of claim 11 , further comprising applying data representing the estimated heat distribution within the object as an input to a finite element analysis to obtain an estimate of physical distortions to the object caused by the heat distribution.

17. The system of claim 11 , wherein converting the model of the object into the node representation of the object comprises generating the nodes of the node representation by randomly sampling spatial locations within the model.

18. The system of claim 11 , wherein generating the adjacency matrix of the object comprises, for each node, determining pairwise distances between the node and neighboring nodes that within a neighbor distance, ε, of the node.

19. The system of claim 11 , wherein generating the adjacency matrix of the object comprises determining a matrix weight, a ij , for each pair of nodes that are within a neighbor distance, ε, of each other.

20. A non-transitory computer readable storage device storing instructions that, when executed by at least one processor, cause the at least one processor to perform operations comprising:

converting a model of an object into a three-dimensional node representation of the object, wherein the node representation includes one or more layers of nodes, and wherein each layer of the one or more layers of nodes corresponds to a layer of material to be added in an additive manufacturing process;

generating, using distances between nodes of the node representation, an adjacency matrix of the object, wherein the adjacency matrix represents each of the one or more layers of nodes in the node representation;

simulating an additive manufacturing process of the object, the simulating comprising, for each layer of the one or more layers of nodes represented in the adjacency matrix:

applying a simulated heat to the layer of the adjacency matrix, and

estimating, using the adjacency matrix, a diffusion of heat to other nodes based on the applied simulated heat; and

generating a representation of an estimated heat distribution within the object.