The invention claimed is:1. One or more non-transitory computer-readable media storing instructions that, when executed by one or more processors, cause the one or more processors to generate an approximate solution to a design problem, by performing the steps of:generating design problem geometry associated with a design problem;synthesizing a problem specification based on the design problem geometry and a set of design criteria;determining that the problem specification satisfies minimum input requirements for a first solution engine resident within a client computing device;executing the first solution engine to generate an approximate solution to the problem specification, wherein the approximate solution includes a first set of design solutions;displaying, via a graphical user interface (GUI), the approximate solution; andafter displaying the approximate solution, transmitting the problem specification to a second solution engine resident within a server machine to generate a second set of design solutions, wherein the second solution engine expends greater computational resources to generate design solutions than the first solution engine.2. The one or more non-transitory computer-readable media of claim 1, wherein generating the design problem geometry comprises receiving at least one input indicating at least one location on the design problem geometry where a force is to be applied.3. The one or more non-transitory computer-readable media of claim 1, further comprising:identifying reference geometry that is geometrically similar to the design problem geometry; andassociating the reference geometry with the design problem geometry.4. The one or more non-transitory computer-readable media of claim 3, further comprising determining at least one force associated with a design constraint that is applied to the reference geometry.5. The one or more non-transitory computer-readable media of claim 1, wherein the set of design criteria includes at least one of a design objective, a design constraint, and a boundary condition.6. The one or more non-transitory computer-readable media of claim 1, further comprising:determining that a first version of the problem specification does not satisfy the minimum input requirements for the solution engine;determining a modification to the first version of the problem specification that would cause the problem specification to satisfy the minimum input requirements for the solution engine; andincorporating the modification into the first version of the problem specification to generate a problem specification that satisfies the minimum input requirements for the solution engine.7. The one or more non-transitory computer-readable media of claim 1, wherein each possible design solution associated with the approximate solution partially meets the set of design criteria.8. The one or more non-transitory computer-readable media of claim 1, wherein each design solution included in the second set of design solutions meets the set of design criteria.9. The one or more non-transitory computer-readable media of claim 8, wherein the second solution engine resident within the server machine generates design solutions having greater accuracy than the design solutions generated by the first solution engine resident within the client computing device.10. The one or more non-transitory computer-readable media of claim 8, wherein the first solution engine resident within the client computing device generates possible design solutions with greater speed than the second solution engine resident within the server machine generates design solutions.11. A computer-implemented method for generating an approximate solution to a design problem, the method comprising:generating design problem geometry associated with a design problem;synthesizing a problem specification based on the design problem geometry and a set of design criteria;determining that the problem specification satisfies minimum input requirements for a first solution engine resident within a client computing device;executing the first solution engine to generate an approximate solution to the problem specification, wherein the approximate solution includes a first set of design solutions;displaying, via a graphical user interface (GUI), the approximate solution; andafter displaying the approximate solution, transmitting the problem specification to a second solution engine resident within a server machine to generate a second set of design solutions, wherein the second solution engine expends greater computational resources to generate design solutions than the first solution engine.12. The computer-implemented method of claim 11, wherein generating the design problem geometry comprises receiving at least one input indicating at least one location on the design problem geometry where a force is to be applied.13. The computer-implemented method of claim 11, further comprising:identifying reference geometry that is geometrically similar to the design problem geometry; andassociating the reference geometry with the design problem geometry.14. The computer-implemented method of claim 13, further comprising determining at least one force associated with a design constraint that is applied to the reference geometry.15. The computer-implemented method of claim 11, wherein the set of design criteria includes at least one of a design objective, a design constraint, and a boundary condition.16. The computer-implemented method of claim 11, further comprising:determining that a first version of the problem specification does not satisfy the minimum input requirements for the solution engine;determining a modification to the first version of the problem specification that would cause the problem specification to satisfy the minimum input requirements for the solution engine; andincorporating the modification into the first version of the problem specification to generate a problem specification that satisfies the minimum input requirements for the solution engine.17. The computer-implemented method of claim 11, wherein each possible design solution associated with the approximate solution partially meets the set of design criteria.18. The computer-implemented method of claim 11, wherein each design solution included in the second set of design solutions meets the set of design criteria.19. The computer-implemented method of claim 18, wherein the second solution engine resident within the server machine generates design solutions having greater accuracy than the possible design solutions generated by the first solution engine resident within the client computing device.20. The computer-implemented method of claim 18, wherein the first solution engine resident within the client computing device generates possible design solutions with greater speed than the second solution engine resident within the server machine generates design solutions.21. A system configured to generate an approximate solution to a design problem, comprising:a memory storing a design application; anda processor that, when executing the design application, is configured to:generate design problem geometry associated with a design problem;synthesize a problem specification based on the design problem geometry and a set of design criteria;determine that the problem specification satisfies minimum input requirements for a first solution engine resident within the memory;execute the first solution engine to generate an approximate solution to the problem specification, wherein the approximate solution includes a first set of design solutions;display, via a graphical user interface (GUI), the approximate solution; andafter displaying the approximate solution, transmit the problem specification to a second solution engine resident within a server machine to generate a second set of design solutions, wherein the second solution engine expends greater computational resources to generate design solutions than the first solution engine.22. The system of claim 21, wherein the processor further configured to determine that a first version of the problem specification does not satisfy the minimum input requirements for the solution engine;determine a modification to the first version of the problem specification that would cause the problem specification to satisfy the minimum input requirements for the solution engine; andincorporate the modification into the first version of the problem specification to generate a problem specification that satisfies the minimum input requirements for the solution engine.23. The one or more non-transitory computer-readable media of claim 1, wherein the design problem geometry comprises a three-dimensional (3D) geometry.