System and method for finite element analysis in the presence of concave elements and method of testing or manufacturing products using same

A method for assessing a product or product design comprising:

• receiving a set of physical parameters to be applied to the product or production design;
• accessing a mesh of finite elements of a product or product design, wherein the mesh of finite elements include tangles;
• for elements in the mesh of finite elements, identifying positive and negative parametric regions;
• for tangled elements in the mesh of finite elements, relaxing a constraint of full invertibility between the positive and negative parametric regions to piecewise invertibility to decompose the tangled elements into invertible regions;
• performing an analysis of the product or product design using the mesh of finite elements with the tangled elements decomposed into the invertible regions and the set of physical parameters;
• and
• generating a report indicating a performance of the product or product design under the set of physical parameters.

A non-transitory computer-readable storage medium having instructions stored thereon that, when executed by a computer processor, causes the computer process to carry out a method for analysis of a product or product design including steps comprising:

• receiving a set of physical parameters and a mesh of elements of a product or product design, wherein the mesh of elements include tangles;
• for elements in the mesh of elements, identifying positive and negative parametric regions;
• for tangled elements in the mesh of elements, relaxing a constraint of full invertibility between the positive and negative parametric regions to piecewise invertibility to decompose the tangled elements into invertible regions;
• performing an analysis of the product or product design using the mesh of elements with the tangled elements decomposed into the invertible regions and the set of physical parameters;
• and
• generating a report indicating a performance of the product or product design under the set of physical parameters.