/**
 * Superconvergent Patch Recovery (SPR) — Zienkiewicz & Zhu (1992)
 *
 * Recovers continuous, superconvergent nodal stresses from per-Gauss-point
 * stress data using least-squares polynomial fitting over element patches.
 *
 * For TET10 elements:
 *   - Gauss points are superconvergent sampling locations
 *   - Polynomial basis: P = [1, x, y, z, xy, xz, yz, x², y², z²] (10 terms)
 *   - Each patch = all elements sharing a node → ~4-20 Gauss points
 *   - Least-squares solve: A·a = b where A = Σ P(xg)·P(xg)��, b = Σ P(xg)·σ(xg)
 *   - Evaluate polynomial at the node: σ*(node) = P(x_node)ᵀ · a
 *
 * References:
 *   O.C. Zienkiewicz & J.Z. Zhu, "The superconvergent patch recovery and
 *   a posteriori error estimates", Int. J. Numer. Meth. Engng., 1992.
 */
export interface SPRResult {
    /** Recovered nodal stress: nodeCount × 6 components [sxx,syy,szz,txy,tyz,txz] */
    nodalStress: Float64Array;
    /** Per-element error indicator η_e = ||σ* - σ_h||_e (if computed) */
    elementError?: Float64Array;
}
/**
 * Build inverse mapping: for each node, which elements contain it.
 * O(nodeCount + elementCount × nodesPerElement) construction.
 */
export declare function buildNodeToElements(tetrahedra: Uint32Array, nodeCount: number, nodesPerElement: number): Uint32Array[];
/**
 * Perform SPR stress recovery for TET10 elements.
 *
 * @param tetrahedra Element connectivity (10 nodes per element)
 * @param vertices Node coordinates (x,y,z per node)
 * @param gaussPointStress Per-GP stress: (elemCount×4)×6 components
 * @param gaussPointCoords Per-GP coordinates: (elemCount×4)×3
 * @param nodeCount Total number of nodes
 * @returns SPRResult with continuous nodal stress field
 */
export declare function recoverNodalStressSPR(tetrahedra: Uint32Array, vertices: Float64Array | Float32Array, gaussPointStress: Float64Array, gaussPointCoords: Float64Array, nodeCount: number): SPRResult;
/**
 * Compute nodal von Mises stress from SPR-recovered nodal Cauchy stress.
 * @param nodalStress nodeCount × 6 Cauchy components
 * @param nodeCount Number of nodes
 * @returns nodeCount × 1 von Mises values
 */
export declare function nodalVonMises(nodalStress: Float64Array, nodeCount: number): Float64Array;
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